我们用tensorflow2来看一个服饰数据集的识别。

 import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers if __name__ == "__main__": fashion_mnist = keras.datasets.fashion_mnist (x_train_all, y_train_all), (x_test, y_test) = fashion_mnist.load_data() x_valid, x_train = x_train_all[:5000], x_train_all[5000:] y_valid, y_train = y_train_all[:5000], y_train_all[5000:] print(x_valid.shape, y_valid.shape) print(x_train.shape, y_train.shape) print(x_test.shape, y_test.shape) def show_single_image(img_arr): plt.imshow(img_arr, cmap='binary') plt.show() show_single_image(x_train[1])

运行结果

 (5000, 28, 28) (5000,) (55000, 28, 28) (55000,) (10000, 28, 28) (10000,)

这里我们可以看到，这些图像数据集都是28*28的单通道图片。我们将这些数据集分成了55000个训练数据集，5000个验证数据集以及10000个测试数据集。现在我们再来看一下这些数据集的分类类型

 import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers if __name__ == "__main__": fashion_mnist = keras.datasets.fashion_mnist (x_train_all, y_train_all), (x_test, y_test) = fashion_mnist.load_data() x_valid, x_train = x_train_all[:5000], x_train_all[5000:] y_valid, y_train = y_train_all[:5000], y_train_all[5000:] # print(x_valid.shape, y_valid.shape)  # print(x_train.shape, y_train.shape)  # print(x_test.shape, y_test.shape)   def show_single_image(img_arr): plt.imshow(img_arr, cmap='binary') plt.show() # show_single_image(x_train[1])   def show_imgs(n_rows, n_cols, x, y, class_names): assert len(x) == len(y) assert n_rows * n_cols < len(x) plt.figure(figsize=(n_cols * 1.4, n_rows * 1.6)) for row in range(n_rows): for col in range(n_cols): index = n_cols * row + col plt.subplot(n_rows, n_cols, index + 1) plt.imshow(x[index], cmap='binary', interpolation='nearest') plt.axis('off') plt.title(class_names[y[index]]) plt.show() #  class_names = ['T-shirt', 'Trouser', 'Pullover', 'Dress', 'Coat', 'Sandal',  'Shirt', 'Sneaker', 'Bag', 'Ankle boot'] show_imgs(3, 5, x_train, y_train, class_names)

运行结果

这里我们可以看到这些服饰总共有10种类型。现在我们就使用神经网络来对这些数据进行训练和验证

 import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers import pandas as pd import os if __name__ == "__main__": os.environ['KMP_DUPLICATE_LIB_OK'] = 'True'  fashion_mnist = keras.datasets.fashion_mnist (x_train_all, y_train_all), (x_test, y_test) = fashion_mnist.load_data() x_valid, x_train = x_train_all[:5000], x_train_all[5000:] y_valid, y_train = y_train_all[:5000], y_train_all[5000:] # print(x_valid.shape, y_valid.shape)  # print(x_train.shape, y_train.shape)  # print(x_test.shape, y_test.shape)   def show_single_image(img_arr): plt.imshow(img_arr, cmap='binary') plt.show() # show_single_image(x_train[1])   def show_imgs(n_rows, n_cols, x, y, class_names): assert len(x) == len(y) assert n_rows * n_cols < len(x) plt.figure(figsize=(n_cols * 1.4, n_rows * 1.6)) for row in range(n_rows): for col in range(n_cols): index = n_cols * row + col plt.subplot(n_rows, n_cols, index + 1) plt.imshow(x[index], cmap='binary', interpolation='nearest') plt.axis('off') plt.title(class_names[y[index]]) plt.show() #  class_names = ['T-shirt', 'Trouser', 'Pullover', 'Dress', 'Coat', 'Sandal',  'Shirt', 'Sneaker', 'Bag', 'Ankle boot'] # show_imgs(3, 5, x_train, y_train, class_names)  model = keras.models.Sequential([ keras.layers.Flatten(input_shape=[28, 28]),  keras.layers.Dense(300, activation='relu'),  keras.layers.Dense(100, activation='relu'),  keras.layers.Dense(10, activation='softmax') ]) # 使用交叉熵损失函数，随机梯度下降法进行训练  # 这里需要说明的是如果是categorical_crossentropy  # 则需要将标签数据集进行one_hot处理，如果是sparse_categorical_crossentropy，  # 则不需要  model.compile(loss=tf.losses.sparse_categorical_crossentropy,  optimizer=optimizers.SGD(learning_rate=0.001),  metrics=['accuracy']) history = model.fit(x_train, y_train, epochs=10, validation_data=(x_valid, y_valid)) print(model.summary()) print(history.history) def plot_learning_curves(history): pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history)

运行结果

 Train on 55000 samples, validate on 5000 samples Epoch 1/10 55000/55000 [==============================] - 6s 107us/sample - loss: 2.2443 - accuracy: 0.7192 - val_loss: 0.6124 - val_accuracy: 0.7928 Epoch 2/10 55000/55000 [==============================] - 5s 95us/sample - loss: 0.5678 - accuracy: 0.7980 - val_loss: 0.5467 - val_accuracy: 0.8018 Epoch 3/10 55000/55000 [==============================] - 5s 92us/sample - loss: 0.4991 - accuracy: 0.8188 - val_loss: 0.4968 - val_accuracy: 0.8358 Epoch 4/10 55000/55000 [==============================] - 5s 97us/sample - loss: 0.4646 - accuracy: 0.8316 - val_loss: 0.4910 - val_accuracy: 0.8332 Epoch 5/10 55000/55000 [==============================] - 7s 119us/sample - loss: 0.4371 - accuracy: 0.8393 - val_loss: 0.4768 - val_accuracy: 0.8374 Epoch 6/10 55000/55000 [==============================] - 7s 123us/sample - loss: 0.4211 - accuracy: 0.8455 - val_loss: 0.4608 - val_accuracy: 0.8444 Epoch 7/10 55000/55000 [==============================] - 6s 103us/sample - loss: 0.4046 - accuracy: 0.8504 - val_loss: 0.4506 - val_accuracy: 0.8464 Epoch 8/10 55000/55000 [==============================] - 5s 97us/sample - loss: 0.3902 - accuracy: 0.8550 - val_loss: 0.4427 - val_accuracy: 0.8480 Epoch 9/10 55000/55000 [==============================] - 5s 97us/sample - loss: 0.3796 - accuracy: 0.8581 - val_loss: 0.4814 - val_accuracy: 0.8312 Epoch 10/10 55000/55000 [==============================] - 5s 99us/sample - loss: 0.3714 - accuracy: 0.8608 - val_loss: 0.4665 - val_accuracy: 0.8440 Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= flatten (Flatten) (None, 784) 0 _________________________________________________________________ dense (Dense) (None, 300) 235500 _________________________________________________________________ dense_1 (Dense) (None, 100) 30100 _________________________________________________________________ dense_2 (Dense) (None, 10) 1010 ================================================================= Total params: 266,610 Trainable params: 266,610 Non-trainable params: 0 _________________________________________________________________ None {'loss': [2.2442730520161716, 0.5677844335772775, 0.49907195046598263, 0.46455069565122775, 0.43706936968456617, 0.4210625493981621, 0.4045901944290508, 0.3901773897236044, 0.3795636681730097, 0.37135513420971955], 'accuracy': [0.71916366, 0.7979818, 0.8187636, 0.83156365, 0.8393091, 0.84549093, 0.8503636, 0.8550182, 0.8580545, 0.8608364], 'val_loss': [0.6123501856803895, 0.5466709545612335, 0.4968059474229813, 0.49100303683280944, 0.4768493502855301, 0.46080493590831756, 0.4505628205776215, 0.44266556935310364, 0.4814212405562401, 0.4664571787118912], 'val_accuracy': [0.7928, 0.8018, 0.8358, 0.8332, 0.8374, 0.8444, 0.8464, 0.848, 0.8312, 0.844]} 

这里我们使用了三个全连接层来构建神经网络，对验证数据集的准确率达到了85.92%。这里我们使用的是随机梯度下降法，关于随机梯度下降法的内容请参考机器学习算法整理 中的随机梯度下降法。下面这个报告是告诉我们在神经网络中每一个全连接层的维度以及参数量。由于我们的图像是28*28，所以扁平化处理后是28*28=784个维度。经过全连接层之后，我们要把第一个全连接层的输出变成样本数*300个维度的矩阵，我们需要将矩阵[样本数，784]•[784, 300]的矩阵W(有关矩阵乘法的内容请参考线性代数整理 中矩阵和矩阵的乘法)，一般我们会加上一个b，就是一个长度为300的向量。这样就得到了一个[样本数, 300]的输出矩阵。而参数量就等于784*300+300=235500。同理，第二个全连接层的输出为样本数*100的矩阵，我们需要将第一层的输出矩阵[样本数, 300]•[300, 100]+b，就得到[样本数, 100]的输出，参数量即为300*100+100=30100。而图中也显示出损失函数值是在稳固下降的，而识别准确率是在稳固上升的。现在我们来给训练数据加上归一化处理。我们先来看一下归一化前后训练数据集的最大值和最小值

 import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers import pandas as pd import os from sklearn.preprocessing import StandardScaler if __name__ == "__main__": os.environ['KMP_DUPLICATE_LIB_OK'] = 'True'  fashion_mnist = keras.datasets.fashion_mnist (x_train_all, y_train_all), (x_test, y_test) = fashion_mnist.load_data() x_valid, x_train = x_train_all[:5000], x_train_all[5000:] y_valid, y_train = y_train_all[:5000], y_train_all[5000:] # print(x_valid.shape, y_valid.shape)  # print(x_train.shape, y_train.shape)  # print(x_test.shape, y_test.shape)  print(np.max(x_train), np.min(x_train)) scaler = StandardScaler() # 归一化过程中，需要将三维图片数据转成二维数据[None, 28, 28] -> [None, 784]  # 归一化结束之后再转回三维图片数据,这里fit_transform会记录训练数据集的均值和方差  x_train = scaler.fit_transform(x_train.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # 这里验证数据集会采用训练数据集的均值和方差  x_valid = scaler.transform(x_valid.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) x_test = scaler.transform(x_test.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) print(np.max(x_train), np.min(x_train))

运行结果

 255 0 2.0231433 -0.8105136

这里我们可以看到，训练数据集归一化前后它们的最大值最小值是不同的。

 import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers import pandas as pd import os from sklearn.preprocessing import StandardScaler if __name__ == "__main__": os.environ['KMP_DUPLICATE_LIB_OK'] = 'True'  fashion_mnist = keras.datasets.fashion_mnist (x_train_all, y_train_all), (x_test, y_test) = fashion_mnist.load_data() x_valid, x_train = x_train_all[:5000], x_train_all[5000:] y_valid, y_train = y_train_all[:5000], y_train_all[5000:] # print(x_valid.shape, y_valid.shape)  # print(x_train.shape, y_train.shape)  # print(x_test.shape, y_test.shape)  # print(np.max(x_train), np.min(x_train))   scaler = StandardScaler() # 归一化过程中，需要将三维图片数据转成二维数据[None, 28, 28] -> [None, 784]  # 归一化结束之后再转回三维图片数据,这里fit_transform会记录训练数据集的均值和方差  x_train = scaler.fit_transform(x_train.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # 这里验证数据集会采用训练数据集的均值和方差  x_valid = scaler.transform(x_valid.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) x_test = scaler.transform(x_test.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # print(np.max(x_train), np.min(x_train))   def show_single_image(img_arr): plt.imshow(img_arr, cmap='binary') plt.show() # show_single_image(x_train[1])   def show_imgs(n_rows, n_cols, x, y, class_names): assert len(x) == len(y) assert n_rows * n_cols < len(x) plt.figure(figsize=(n_cols * 1.4, n_rows * 1.6)) for row in range(n_rows): for col in range(n_cols): index = n_cols * row + col plt.subplot(n_rows, n_cols, index + 1) plt.imshow(x[index], cmap='binary', interpolation='nearest') plt.axis('off') plt.title(class_names[y[index]]) plt.show() #  class_names = ['T-shirt', 'Trouser', 'Pullover', 'Dress', 'Coat', 'Sandal',  'Shirt', 'Sneaker', 'Bag', 'Ankle boot'] # show_imgs(3, 5, x_train, y_train, class_names)  model = keras.models.Sequential([ keras.layers.Flatten(input_shape=[28, 28]),  keras.layers.Dense(300, activation='relu'),  keras.layers.Dense(100, activation='relu'),  keras.layers.Dense(10, activation='softmax') ]) # 使用交叉熵损失函数，随机梯度下降法进行训练  # 这里需要说明的是如果是categorical_crossentropy  # 则需要将标签数据集进行one_hot处理，如果是sparse_categorical_crossentropy，  # 则不需要  model.compile(loss=tf.losses.sparse_categorical_crossentropy,  optimizer=optimizers.SGD(learning_rate=0.001),  metrics=['accuracy']) history = model.fit(x_train, y_train, epochs=10, validation_data=(x_valid, y_valid)) print(model.evaluate(x_test, y_test)) print(model.summary()) print(history.history) def plot_learning_curves(history): pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history)

运行结果

 Train on 55000 samples, validate on 5000 samples Epoch 1/10 55000/55000 [==============================] - 5s 95us/sample - loss: 0.9122 - accuracy: 0.7003 - val_loss: 0.6157 - val_accuracy: 0.7920 Epoch 2/10 55000/55000 [==============================] - 5s 83us/sample - loss: 0.5771 - accuracy: 0.8010 - val_loss: 0.5165 - val_accuracy: 0.8182 Epoch 3/10 55000/55000 [==============================] - 6s 104us/sample - loss: 0.5075 - accuracy: 0.8235 - val_loss: 0.4732 - val_accuracy: 0.8378 Epoch 4/10 55000/55000 [==============================] - 7s 127us/sample - loss: 0.4716 - accuracy: 0.8343 - val_loss: 0.4473 - val_accuracy: 0.8480 Epoch 5/10 55000/55000 [==============================] - 6s 117us/sample - loss: 0.4477 - accuracy: 0.8421 - val_loss: 0.4323 - val_accuracy: 0.8530 Epoch 6/10 55000/55000 [==============================] - 6s 110us/sample - loss: 0.4306 - accuracy: 0.8483 - val_loss: 0.4175 - val_accuracy: 0.8580 Epoch 7/10 55000/55000 [==============================] - 5s 90us/sample - loss: 0.4167 - accuracy: 0.8521 - val_loss: 0.4101 - val_accuracy: 0.8564 Epoch 8/10 55000/55000 [==============================] - 5s 90us/sample - loss: 0.4059 - accuracy: 0.8562 - val_loss: 0.4022 - val_accuracy: 0.8626 Epoch 9/10 55000/55000 [==============================] - 5s 92us/sample - loss: 0.3964 - accuracy: 0.8599 - val_loss: 0.3944 - val_accuracy: 0.8634 Epoch 10/10 55000/55000 [==============================] - 5s 93us/sample - loss: 0.3880 - accuracy: 0.8630 - val_loss: 0.3889 - val_accuracy: 0.8606 10000/1 ==============================================] - 1s 51us/sample - loss: 0.2991 - accuracy: 0.8472 [0.43079993045330045, 0.8472] Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= flatten (Flatten) (None, 784) 0 _________________________________________________________________ dense (Dense) (None, 300) 235500 _________________________________________________________________ dense_1 (Dense) (None, 100) 30100 _________________________________________________________________ dense_2 (Dense) (None, 10) 1010 ================================================================= Total params: 266,610 Trainable params: 266,610 Non-trainable params: 0 _________________________________________________________________ None {'loss': [0.912204550890489, 0.5771390253067017, 0.507524390927228, 0.4716112705404108, 0.4477458443338221, 0.4306134765581651, 0.416733508162065, 0.4059152506828308, 0.3963754140810533, 0.38801397878473454], 'accuracy': [0.70034546, 0.801, 0.82345456, 0.8343091, 0.84214544, 0.84827274, 0.85214543, 0.85623634, 0.8598727, 0.8629818], 'val_loss': [0.615698953294754, 0.516535887670517, 0.47322214045524597, 0.4472690547943115, 0.43233813087940215, 0.41751169788837433, 0.41005783474445345, 0.40220267939567567, 0.3943846334218979, 0.38885269825458524], 'val_accuracy': [0.792, 0.8182, 0.8378, 0.848, 0.853, 0.858, 0.8564, 0.8626, 0.8634, 0.8606]}

这里我们对测试数据集进行了测试，它的分类准确率达到了84.72%。

回调函数

回调函数是当我们在训练模型的时候，中间可能要做一些事情。比如说模型训练中，当损失函数值loss不再下降的时候，我们可以提前停止训练。又比如在训练的过程中，每隔段时间把模型参数给保存下来。又或者在模型训练过程中，就对一些模型指标进行图形化输出等等。

 import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers import pandas as pd import os from sklearn.preprocessing import StandardScaler if __name__ == "__main__": os.environ['KMP_DUPLICATE_LIB_OK'] = 'True'  fashion_mnist = keras.datasets.fashion_mnist (x_train_all, y_train_all), (x_test, y_test) = fashion_mnist.load_data() x_valid, x_train = x_train_all[:5000], x_train_all[5000:] y_valid, y_train = y_train_all[:5000], y_train_all[5000:] # print(x_valid.shape, y_valid.shape)  # print(x_train.shape, y_train.shape)  # print(x_test.shape, y_test.shape)  # print(np.max(x_train), np.min(x_train))   scaler = StandardScaler() # 归一化过程中，需要将三维图片数据转成二维数据[None, 28, 28] -> [None, 784]  # 归一化结束之后再转回三维图片数据,这里fit_transform会记录训练数据集的均值和方差  x_train = scaler.fit_transform(x_train.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # 这里验证数据集会采用训练数据集的均值和方差  x_valid = scaler.transform(x_valid.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) x_test = scaler.transform(x_test.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # print(np.max(x_train), np.min(x_train))   def show_single_image(img_arr): plt.imshow(img_arr, cmap='binary') plt.show() # show_single_image(x_train[1])   def show_imgs(n_rows, n_cols, x, y, class_names): assert len(x) == len(y) assert n_rows * n_cols < len(x) plt.figure(figsize=(n_cols * 1.4, n_rows * 1.6)) for row in range(n_rows): for col in range(n_cols): index = n_cols * row + col plt.subplot(n_rows, n_cols, index + 1) plt.imshow(x[index], cmap='binary', interpolation='nearest') plt.axis('off') plt.title(class_names[y[index]]) plt.show() #  class_names = ['T-shirt', 'Trouser', 'Pullover', 'Dress', 'Coat', 'Sandal',  'Shirt', 'Sneaker', 'Bag', 'Ankle boot'] # show_imgs(3, 5, x_train, y_train, class_names)  model = keras.models.Sequential([ keras.layers.Flatten(input_shape=[28, 28]),  keras.layers.Dense(300, activation='relu'),  keras.layers.Dense(100, activation='relu'),  keras.layers.Dense(10, activation='softmax') ]) # 使用交叉熵损失函数，随机梯度下降法进行训练  # 这里需要说明的是如果是categorical_crossentropy  # 则需要将标签数据集进行one_hot处理，如果是sparse_categorical_crossentropy，  # 则不需要  model.compile(loss=tf.losses.sparse_categorical_crossentropy,  optimizer=optimizers.SGD(learning_rate=0.001),  metrics=['accuracy']) # 我们这里使用三个回调函数Tensorboard, earlystopping, ModelCheckpoint  logdir = "./callbacks"  if not os.path.exists(logdir): os.mkdir(logdir) output_model_file = os.path.join(logdir, "fashion_mnist_model.h5") callbacks = [ # TensorBoard可以保存我们在训练中的指标，比如损失函数值以及识别准确率  keras.callbacks.TensorBoard(logdir),  # ModelCheckpoint是保存模型参数  keras.callbacks.ModelCheckpoint(output_model_file, save_best_only=True),  # EarlyStopping是提前终止训练  keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3) ] history = model.fit(x_train, y_train, epochs=10,  validation_data=(x_valid, y_valid),  callbacks=callbacks) print(model.evaluate(x_test, y_test)) print(model.summary()) # print(history.history)   # def plot_learning_curves(history):  # pd.DataFrame(history.history).plot(figsize=(8, 5))  # plt.grid(True)  # plt.gca().set_ylim(0, 1)  # plt.show()  #  # plot_learning_curves(history)

当我们训练完成之后，可以到callbacks上一层文件夹中，展开callbacks文件夹，我们可以看到这样一些文件

在callbacks上一层文件夹中输入命令

 (base) -bash-3.2$ tensorboard --logdir=callbacks

会得到这样一些输出

 Serving TensorBoard on localhost; to expose to the network, use a proxy or pass --bind_all TensorBoard 2.0.0 at http://localhost:6006/ (Press CTRL+C to quit)

此时打开浏览器访问http://localhost:6006，会看到我们训练中的指标数据图

以及神经网络的层级图

而EarlyStopping的参数意义如下：

1. min_delta：增大或减小的阈值，只有大于这个部分才算作improvement(改善)。这个值的大小取决于monitor，也反映了你的容忍程度。例如monitor(监控)是’acc’，同时其变化范围在70%-90%之间，所以对于小于0.01%的变化不关心。加上观察到训练过程中存在抖动的情况（即先下降后上升），所以适当增大容忍程度，最终设为0.001%。
2. patience：能够容忍多少个epoch内都没有improvement。这个设置其实是在抖动和真正的准确率下降之间做tradeoff(权衡)。如果patience设的大，那么最终得到的准确率要略低于模型可以达到的最高准确率。如果patience设的小，那么模型很可能在前期抖动，还在全图搜索的阶段就停止了，准确率一般很差。patience的大小和learning rate直接相关。在learning rate设定的情况下，前期先训练几次观察抖动的epoch number，比其稍大些设置patience。在learning rate变化的情况下，建议要略小于最大的抖动epoch number。笔者在引入EarlyStopping之前就已经得到可以接受的结果了，EarlyStopping算是锦上添花，所以patience设的比较高，设为抖动epoch number的最大值。
3. min_delta和patience都和“避免模型停止在抖动过程中”有关系，所以调节的时候需要互相协调。通常情况下，min_delta降低，那么patience可以适当减少；min_delta增加，那么patience需要适当延长；反之亦然。

归一化与批归一化

• 归一化

1. Min-max归一化：x*=(x-min)/(max-min)
2. Z-score归一化：x*=(x-μ)/δ，这里μ表示均值，δ表示方差，是我们经常使用的归一化

• 批归一化

批归一化是指把归一化这种思路从输入数据上给扩展到网络的每层的激活值上，每层的激活值都做归一化。我们知道对于神经网络来说是一种层级结构，每一层的输出就是下一层的输入，我们在每一层的输入上都去做归一化，那么就会使得整个的网络的效果会更好。

 import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers import pandas as pd import os from sklearn.preprocessing import StandardScaler if __name__ == "__main__": os.environ['KMP_DUPLICATE_LIB_OK'] = 'True'  fashion_mnist = keras.datasets.fashion_mnist (x_train_all, y_train_all), (x_test, y_test) = fashion_mnist.load_data() x_valid, x_train = x_train_all[:5000], x_train_all[5000:] y_valid, y_train = y_train_all[:5000], y_train_all[5000:] # print(x_valid.shape, y_valid.shape)  # print(x_train.shape, y_train.shape)  # print(x_test.shape, y_test.shape)  # print(np.max(x_train), np.min(x_train))   scaler = StandardScaler() # 归一化过程中，需要将三维图片数据转成二维数据[None, 28, 28] -> [None, 784]  # 归一化结束之后再转回三维图片数据,这里fit_transform会记录训练数据集的均值和方差  x_train = scaler.fit_transform(x_train.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # 这里验证数据集会采用训练数据集的均值和方差  x_valid = scaler.transform(x_valid.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) x_test = scaler.transform(x_test.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # print(np.max(x_train), np.min(x_train))   def show_single_image(img_arr): plt.imshow(img_arr, cmap='binary') plt.show() # show_single_image(x_train[1])   def show_imgs(n_rows, n_cols, x, y, class_names): assert len(x) == len(y) assert n_rows * n_cols < len(x) plt.figure(figsize=(n_cols * 1.4, n_rows * 1.6)) for row in range(n_rows): for col in range(n_cols): index = n_cols * row + col plt.subplot(n_rows, n_cols, index + 1) plt.imshow(x[index], cmap='binary', interpolation='nearest') plt.axis('off') plt.title(class_names[y[index]]) plt.show() #  class_names = ['T-shirt', 'Trouser', 'Pullover', 'Dress', 'Coat', 'Sandal',  'Shirt', 'Sneaker', 'Bag', 'Ankle boot'] # show_imgs(3, 5, x_train, y_train, class_names)  model = keras.models.Sequential([ keras.layers.Flatten(input_shape=[28, 28]),  keras.layers.Dense(300, activation='relu'),  # 批归一化  keras.layers.BatchNormalization(),  keras.layers.Dense(100, activation='relu'),  keras.layers.BatchNormalization(),  keras.layers.Dense(10, activation='softmax') # 上面是将批归一化放在激活函数之后，也可以放在激活函数之前  # keras.layers.Dense(300),  # keras.layers.BatchNormalization(),  # keras.layers.Activation('relu'),  ]) # 使用交叉熵损失函数，随机梯度下降法进行训练  # 这里需要说明的是如果是categorical_crossentropy  # 则需要将标签数据集进行one_hot处理，如果是sparse_categorical_crossentropy，  # 则不需要  model.compile(loss=tf.losses.sparse_categorical_crossentropy,  optimizer=optimizers.SGD(learning_rate=0.001),  metrics=['accuracy']) # 我们这里使用三个回调函数Tensorboard, earlystopping, ModelCheckpoint  logdir = "./callbacks"  if not os.path.exists(logdir): os.mkdir(logdir) output_model_file = os.path.join(logdir, "fashion_mnist_model.h5") callbacks = [ # TensorBoard可以保存我们在训练中的指标，比如损失函数值以及识别准确率  keras.callbacks.TensorBoard(logdir),  # ModelCheckpoint是保存模型参数  keras.callbacks.ModelCheckpoint(output_model_file, save_best_only=True),  # EarlyStopping是提前终止训练  keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3) ] history = model.fit(x_train, y_train, epochs=10,  validation_data=(x_valid, y_valid),  callbacks=callbacks) print(model.evaluate(x_test, y_test)) print(model.summary()) # print(history.history)   # def plot_learning_curves(history):  # pd.DataFrame(history.history).plot(figsize=(8, 5))  # plt.grid(True)  # plt.gca().set_ylim(0, 1)  # plt.show()  #  # plot_learning_curves(history)

运行结果

 Train on 55000 samples, validate on 5000 samples Epoch 1/10 32/55000 [..............................] - ETA: 44:06 - loss: 3.0657 - accuracy: 0.06252021-10-20 23:21:46.915226: I tensorflow/core/profiler/lib/profiler_session.cc:184] Profiler session started. 55000/55000 [==============================] - 12s 223us/sample - loss: 0.8149 - accuracy: 0.7291 - val_loss: 0.5425 - val_accuracy: 0.8172 Epoch 2/10 55000/55000 [==============================] - 11s 195us/sample - loss: 0.5600 - accuracy: 0.8085 - val_loss: 0.4776 - val_accuracy: 0.8398 Epoch 3/10 55000/55000 [==============================] - 13s 229us/sample - loss: 0.5023 - accuracy: 0.8254 - val_loss: 0.4405 - val_accuracy: 0.8514 Epoch 4/10 55000/55000 [==============================] - 12s 216us/sample - loss: 0.4684 - accuracy: 0.8367 - val_loss: 0.4181 - val_accuracy: 0.8600 Epoch 5/10 55000/55000 [==============================] - 11s 200us/sample - loss: 0.4447 - accuracy: 0.8459 - val_loss: 0.4045 - val_accuracy: 0.8634 Epoch 6/10 55000/55000 [==============================] - 11s 200us/sample - loss: 0.4250 - accuracy: 0.8526 - val_loss: 0.3916 - val_accuracy: 0.8688 Epoch 7/10 55000/55000 [==============================] - 11s 204us/sample - loss: 0.4093 - accuracy: 0.8561 - val_loss: 0.3838 - val_accuracy: 0.8692 Epoch 8/10 55000/55000 [==============================] - 11s 207us/sample - loss: 0.3983 - accuracy: 0.8600 - val_loss: 0.3772 - val_accuracy: 0.8718 Epoch 9/10 55000/55000 [==============================] - 11s 207us/sample - loss: 0.3886 - accuracy: 0.8645 - val_loss: 0.3687 - val_accuracy: 0.8732 Epoch 10/10 55000/55000 [==============================] - 12s 212us/sample - loss: 0.3777 - accuracy: 0.8681 - val_loss: 0.3646 - val_accuracy: 0.8742 10000/1 [==================================================] - 1s 99us/sample - loss: 0.3293 - accuracy: 0.8609 [0.39349488220214845, 0.8609] Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= flatten (Flatten) (None, 784) 0 _________________________________________________________________ dense (Dense) (None, 300) 235500 _________________________________________________________________ batch_normalization (BatchNo (None, 300) 1200 _________________________________________________________________ dense_1 (Dense) (None, 100) 30100 _________________________________________________________________ batch_normalization_1 (Batch (None, 100) 400 _________________________________________________________________ dense_2 (Dense) (None, 10) 1010 ================================================================= Total params: 268,210 Trainable params: 267,410 Non-trainable params: 800 _________________________________________________________________ None

通过批过一化后，我们可以看到它的识别准确率比之前都得到了提升。

dropout

有关dropout的详细内容请参考Tensorflow深度学习算法整理

 import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers import pandas as pd import os from sklearn.preprocessing import StandardScaler if __name__ == "__main__": os.environ['KMP_DUPLICATE_LIB_OK'] = 'True'  fashion_mnist = keras.datasets.fashion_mnist (x_train_all, y_train_all), (x_test, y_test) = fashion_mnist.load_data() x_valid, x_train = x_train_all[:5000], x_train_all[5000:] y_valid, y_train = y_train_all[:5000], y_train_all[5000:] # print(x_valid.shape, y_valid.shape)  # print(x_train.shape, y_train.shape)  # print(x_test.shape, y_test.shape)  # print(np.max(x_train), np.min(x_train))   scaler = StandardScaler() # 归一化过程中，需要将三维图片数据转成二维数据[None, 28, 28] -> [None, 784]  # 归一化结束之后再转回三维图片数据,这里fit_transform会记录训练数据集的均值和方差  x_train = scaler.fit_transform(x_train.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # 这里验证数据集会采用训练数据集的均值和方差  x_valid = scaler.transform(x_valid.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) x_test = scaler.transform(x_test.astype(np.float32).reshape(-1, 1)).reshape(-1, 28, 28) # print(np.max(x_train), np.min(x_train))   def show_single_image(img_arr): plt.imshow(img_arr, cmap='binary') plt.show() # show_single_image(x_train[1])   def show_imgs(n_rows, n_cols, x, y, class_names): assert len(x) == len(y) assert n_rows * n_cols < len(x) plt.figure(figsize=(n_cols * 1.4, n_rows * 1.6)) for row in range(n_rows): for col in range(n_cols): index = n_cols * row + col plt.subplot(n_rows, n_cols, index + 1) plt.imshow(x[index], cmap='binary', interpolation='nearest') plt.axis('off') plt.title(class_names[y[index]]) plt.show() #  class_names = ['T-shirt', 'Trouser', 'Pullover', 'Dress', 'Coat', 'Sandal',  'Shirt', 'Sneaker', 'Bag', 'Ankle boot'] # show_imgs(3, 5, x_train, y_train, class_names)  model = keras.models.Sequential([ keras.layers.Flatten(input_shape=[28, 28]),  keras.layers.Dense(300, activation='relu'),  # 批归一化  keras.layers.BatchNormalization(),  keras.layers.Dense(100, activation='relu'),  keras.layers.BatchNormalization(),  # AlphaDropout，1均值和方差不变，2激活值归一化性质不变  keras.layers.AlphaDropout(rate=0.5),  # keras.layers.Dropout(rate=0.5),  keras.layers.Dense(10, activation='softmax') # 上面是将批归一化放在激活函数之后，也可以放在激活函数之前  # keras.layers.Dense(300),  # keras.layers.BatchNormalization(),  # keras.layers.Activation('relu'),  ]) # 使用交叉熵损失函数，随机梯度下降法进行训练  # 这里需要说明的是如果是categorical_crossentropy  # 则需要将标签数据集进行one_hot处理，如果是sparse_categorical_crossentropy，  # 则不需要  model.compile(loss=tf.losses.sparse_categorical_crossentropy,  optimizer=optimizers.SGD(learning_rate=0.001),  metrics=['accuracy']) # 我们这里使用三个回调函数Tensorboard, earlystopping, ModelCheckpoint  logdir = "./callbacks"  if not os.path.exists(logdir): os.mkdir(logdir) output_model_file = os.path.join(logdir, "fashion_mnist_model.h5") callbacks = [ # TensorBoard可以保存我们在训练中的指标，比如损失函数值以及识别准确率  keras.callbacks.TensorBoard(logdir),  # ModelCheckpoint是保存模型参数  keras.callbacks.ModelCheckpoint(output_model_file, save_best_only=True),  # EarlyStopping是提前终止训练  keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3) ] history = model.fit(x_train, y_train, epochs=20,  validation_data=(x_valid, y_valid),  callbacks=callbacks) print(model.evaluate(x_test, y_test)) print(model.summary()) # print(history.history)   # def plot_learning_curves(history):  # pd.DataFrame(history.history).plot(figsize=(8, 5))  # plt.grid(True)  # plt.gca().set_ylim(0, 1)  # plt.show()  #  # plot_learning_curves(history)

运行结果

 Train on 55000 samples, validate on 5000 samples Epoch 1/20 32/55000 [..............................] - ETA: 32:30 - loss: 2.7970 - accuracy: 0.18752021-10-20 23:56:36.685505: I tensorflow/core/profiler/lib/profiler_session.cc:184] Profiler session started. 55000/55000 [==============================] - 14s 252us/sample - loss: 1.6393 - accuracy: 0.4541 - val_loss: 0.7376 - val_accuracy: 0.7648 Epoch 2/20 55000/55000 [==============================] - 12s 222us/sample - loss: 1.1364 - accuracy: 0.6211 - val_loss: 0.6595 - val_accuracy: 0.7934 Epoch 3/20 55000/55000 [==============================] - 15s 275us/sample - loss: 0.9986 - accuracy: 0.6656 - val_loss: 0.6102 - val_accuracy: 0.8088 Epoch 4/20 55000/55000 [==============================] - 14s 257us/sample - loss: 0.9116 - accuracy: 0.6943 - val_loss: 0.5842 - val_accuracy: 0.8180 Epoch 5/20 55000/55000 [==============================] - 13s 232us/sample - loss: 0.8560 - accuracy: 0.7124 - val_loss: 0.5690 - val_accuracy: 0.8248 Epoch 6/20 55000/55000 [==============================] - 12s 227us/sample - loss: 0.8100 - accuracy: 0.7288 - val_loss: 0.5518 - val_accuracy: 0.8328 Epoch 7/20 55000/55000 [==============================] - 13s 230us/sample - loss: 0.7779 - accuracy: 0.7401 - val_loss: 0.5428 - val_accuracy: 0.8372 Epoch 8/20 55000/55000 [==============================] - 13s 229us/sample - loss: 0.7481 - accuracy: 0.7501 - val_loss: 0.5353 - val_accuracy: 0.8414 Epoch 9/20 55000/55000 [==============================] - 12s 225us/sample - loss: 0.7238 - accuracy: 0.7579 - val_loss: 0.5326 - val_accuracy: 0.8420 Epoch 10/20 55000/55000 [==============================] - 12s 222us/sample - loss: 0.6993 - accuracy: 0.7648 - val_loss: 0.5207 - val_accuracy: 0.8458 Epoch 11/20 55000/55000 [==============================] - 12s 222us/sample - loss: 0.6878 - accuracy: 0.7677 - val_loss: 0.5111 - val_accuracy: 0.8478 Epoch 12/20 55000/55000 [==============================] - 13s 230us/sample - loss: 0.6640 - accuracy: 0.7769 - val_loss: 0.5103 - val_accuracy: 0.8474 Epoch 13/20 55000/55000 [==============================] - 13s 243us/sample - loss: 0.6516 - accuracy: 0.7794 - val_loss: 0.5073 - val_accuracy: 0.8494 Epoch 14/20 55000/55000 [==============================] - 13s 237us/sample - loss: 0.6374 - accuracy: 0.7845 - val_loss: 0.5106 - val_accuracy: 0.8528 Epoch 15/20 55000/55000 [==============================] - 13s 234us/sample - loss: 0.6228 - accuracy: 0.7924 - val_loss: 0.5013 - val_accuracy: 0.8534 Epoch 16/20 55000/55000 [==============================] - 13s 231us/sample - loss: 0.6058 - accuracy: 0.7943 - val_loss: 0.4987 - val_accuracy: 0.8558 Epoch 17/20 55000/55000 [==============================] - 13s 237us/sample - loss: 0.5989 - accuracy: 0.7980 - val_loss: 0.4985 - val_accuracy: 0.8556 Epoch 18/20 55000/55000 [==============================] - 13s 232us/sample - loss: 0.5835 - accuracy: 0.8036 - val_loss: 0.4997 - val_accuracy: 0.8566 Epoch 19/20 55000/55000 [==============================] - 13s 237us/sample - loss: 0.5795 - accuracy: 0.8058 - val_loss: 0.4907 - val_accuracy: 0.8596 Epoch 20/20 55000/55000 [==============================] - 13s 230us/sample - loss: 0.5730 - accuracy: 0.8054 - val_loss: 0.4887 - val_accuracy: 0.8606 10000/1 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=] - 1s 81us/sample - loss: 0.4401 - accuracy: 0.8478 [0.564703483581543, 0.8478] Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= flatten (Flatten) (None, 784) 0 _________________________________________________________________ dense (Dense) (None, 300) 235500 _________________________________________________________________ batch_normalization (BatchNo (None, 300) 1200 _________________________________________________________________ dense_1 (Dense) (None, 100) 30100 _________________________________________________________________ batch_normalization_1 (Batch (None, 100) 400 _________________________________________________________________ alpha_dropout (AlphaDropout) (None, 100) 0 _________________________________________________________________ dense_2 (Dense) (None, 10) 1010 ================================================================= Total params: 268,210 Trainable params: 267,410 Non-trainable params: 800 _________________________________________________________________ None

通过对dropout的使用，我们发现这个数据集的过拟合现象并不严重，它的识别准确率比之前反而有所降低。

wide_deep模型

google16年发布，可用于分类和回归

稀疏特征

• 离散值特征，比如说一个人的性别信息，只能从两个值里面去进行选择。即类别类型的特征。
• 可以使用One-hot表示。

比如：专业={计算机,人文,其他}。人文=[0, 1, 0]

比如:  词表={人工智能,你,他,网络,...}，他=[0, 0, 1, 0, ...]

叉乘={(计算机,人工智能),(计算机,你),...}，这里表示"专业"中的每个词跟"词表"中的每个词进行组合。叉乘是可以用来刻画一个样本的。

比如说一个物体的所有特征，我们都把它表示成离散特征，我们就可以用叉乘来精确的刻画一个样本，叉乘可以精确的刻画到所有样本的所有可能性。

• 叉乘之后
  • 稀疏特征做叉乘获取共现信息
  • 实现记忆的效果

如果一个物体可以用离散特征去表达它的全部信息，那么这个物体的总量也是确定的，那么叉乘之后的总的集合包含了所有物体的所有可能性。设想我们有一种非常大的模型，这个模型可以把所有样本都记住。当我们遇到新的样本的时候，那么这个样本肯定也是这个大集合中的一个。所以如果我们的模型能够记住大集合中的每一个样本，那么对于任何新的样本它都可以100%的去进行正确的预测。

稀疏特征——优缺点

• 优点
  • 有效，广泛用于工业界
• 缺点
  • 需要人工设计
  • 可能过拟合，所有特征都叉乘，相当于记住每一个样本
  • 泛化能力差，没出现过就不会起效果

密集特征

• 向量表达

比如：词表={人工智能,你,他,网络,...}，他=[0.3, 0.2, 0.6, (n维向量)]，我们可以用向量之间的距离来表示这两个词对应的距离。

• Word2vec工具

可以参考Tensorflow深度学习算法整理(二) 中的内容

密集特征的优缺点

• 优点
  • 带有语义信息，不同向量之间有相关性
  • 兼容没有出现过的特征组合
  • 更少人工参与
• 缺点
  • 过度泛化，推荐不怎么相关的产品

Wide & Deep模型结构

Wide & Deep Vs Wide

在左边的Wide模型中，我们可以看到它只有一层，输入就是稀疏特征，也就是一个One-hot表达。One-hot表达的每个分量都直接连接到输出单元上去。在右边的Wide & Deep模型，它的左半部分也就是一个Wide模型，它的右半部分是一个Deep模型，这个Deep模型就是有多层的神经网络，在这里，我们将输入的数据表现为一个密集的向量表达，在密集表达之上有一个多层的神经网络，在经过多层神经网络之后再连接到输出的神经单元上去。

Wide & Deep Vs Deep

在这里，右图是一个Deep模型，它跟Wide & Deep模型的区别就在于它没有连接稀疏特征的那一块。

这是google商店中一个推荐算法的模型图，它就是一个典型的Wide & Deep模型，它有很多的特征，其中用户已经安装的软件和展示的软件做了叉乘，作为Wide模型的输入。而其他的特征，有些做了Embedding，有些没有做Embedding，把它们拼接起来，作为一个总的特征(密集表示)，再经过多层的神经网络，形成一个Deep的部分，然后再使用一个逻辑回归的损失函数把Wide和Deep给组合起来。现在我们先来看一个加利福尼亚的一个房价的回归问题

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import time import tensorflow as tf from tensorflow import keras from sklearn.datasets import fetch_california_housing import pprint from sklearn.model_selection import train_test_split if __name__ == "__main__": housing = fetch_california_housing() print(housing.DESCR) print(housing.data.shape) print(housing.target.shape) pprint.pprint(housing.data[0:5]) pprint.pprint(housing.target[0:5]) X_train_all, X_test, y_train_all, y_test = train_test_split(housing.data, housing.target, random_state=7) X_train, X_valid, y_train, y_valid = train_test_split(X_train_all, y_train_all, random_state=11) print(X_train.shape, y_train.shape) print(X_valid.shape, y_valid.shape) print(X_test.shape, y_test.shape)

运行结果

 .. _california_housing_dataset: California Housing dataset -------------------------- **Data Set Characteristics:** :Number of Instances: 20640 :Number of Attributes: 8 numeric, predictive attributes and the target :Attribute Information: - MedInc median income in block - HouseAge median house age in block - AveRooms average number of rooms - AveBedrms average number of bedrooms - Population block population - AveOccup average house occupancy - Latitude house block latitude - Longitude house block longitude :Missing Attribute Values: None This dataset was obtained from the StatLib repository. http://lib.stat.cmu.edu/datasets/ The target variable is the median house value for California districts. This dataset was derived from the 1990 U.S. census, using one row per census block group. A block group is the smallest geographical unit for which the U.S. Census Bureau publishes sample data (a block group typically has a population of 600 to 3,000 people). It can be downloaded/loaded using the :func:`sklearn.datasets.fetch_california_housing` function. .. topic:: References - Pace, R. Kelley and Ronald Barry, Sparse Spatial Autoregressions, Statistics and Probability Letters, 33 (1997) 291-297 (20640, 8) (20640,) array([[ 8.32520000e+00, 4.10000000e+01, 6.98412698e+00, 1.02380952e+00, 3.22000000e+02, 2.55555556e+00, 3.78800000e+01, -1.22230000e+02], [ 8.30140000e+00, 2.10000000e+01, 6.23813708e+00, 9.71880492e-01, 2.40100000e+03, 2.10984183e+00, 3.78600000e+01, -1.22220000e+02], [ 7.25740000e+00, 5.20000000e+01, 8.28813559e+00, 1.07344633e+00, 4.96000000e+02, 2.80225989e+00, 3.78500000e+01, -1.22240000e+02], [ 5.64310000e+00, 5.20000000e+01, 5.81735160e+00, 1.07305936e+00, 5.58000000e+02, 2.54794521e+00, 3.78500000e+01, -1.22250000e+02], [ 3.84620000e+00, 5.20000000e+01, 6.28185328e+00, 1.08108108e+00, 5.65000000e+02, 2.18146718e+00, 3.78500000e+01, -1.22250000e+02]]) array([4.526, 3.585, 3.521, 3.413, 3.422]) (11610, 8) (11610,) (3870, 8) (3870,) (5160, 8) (5160,)

我们可以看到这里有20640条样本数据，维度为8，说明影响房价的有8个特征。其中，我们打印了5条样本数据和标签数据。并将其拆分为训练数据集，验证数据集和测试数据集。现在我们来进行模型训练和打印学习曲线

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import time import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers from sklearn.datasets import fetch_california_housing import pprint from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler if __name__ == "__main__": housing = fetch_california_housing() # print(housing.DESCR)  # print(housing.data.shape)  # print(housing.target.shape)  # pprint.pprint(housing.data[0:5])  # pprint.pprint(housing.target[0:5])  X_train_all, X_test, y_train_all, y_test = train_test_split(housing.data, housing.target, random_state=7) X_train, X_valid, y_train, y_valid = train_test_split(X_train_all, y_train_all, random_state=11) # print(X_train.shape, y_train.shape)  # print(X_valid.shape, y_valid.shape)  # print(X_test.shape, y_test.shape)  scaler = StandardScaler() # 归一化  X_train = scaler.fit_transform(X_train) X_valid = scaler.transform(X_valid) X_test = scaler.transform(X_test) model = keras.models.Sequential([ layers.Dense(30, activation='relu', input_shape=X_train.shape[1:]),  layers.Dense(1) ]) print(model.summary()) # 使用均方误差损失函数和随机梯度下降法  model.compile(loss='mean_squared_error', optimizer=optimizers.SGD(learning_rate=0.01)) callbacks = [keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3)] history = model.fit(X_train, y_train, validation_data=(X_valid, y_valid),  epochs=100, callbacks=callbacks) print(model.evaluate(X_test, y_test)) def plot_learning_curves(history): # 学习曲线  pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history) 

运行结果

 Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= dense (Dense) (None, 30) 270 _________________________________________________________________ dense_1 (Dense) (None, 1) 31 ================================================================= Total params: 301 Trainable params: 301 Non-trainable params: 0 _________________________________________________________________ None Train on 11610 samples, validate on 3870 samples Epoch 1/100 11610/11610 [==============================] - 1s 88us/sample - loss: 1.3027 - val_loss: 2.2434 Epoch 2/100 11610/11610 [==============================] - 1s 45us/sample - loss: 4.6891 - val_loss: 0.4434 Epoch 3/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.4092 - val_loss: 0.3887 Epoch 4/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3811 - val_loss: 0.3797 Epoch 5/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3718 - val_loss: 0.3839 Epoch 6/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3652 - val_loss: 0.3714 Epoch 7/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3620 - val_loss: 0.3662 Epoch 8/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3587 - val_loss: 0.3715 Epoch 9/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3555 - val_loss: 0.3632 Epoch 10/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3525 - val_loss: 0.3620 Epoch 11/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3518 - val_loss: 0.3566 Epoch 12/100 11610/11610 [==============================] - 0s 43us/sample - loss: 0.3486 - val_loss: 0.3544 Epoch 13/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3466 - val_loss: 0.3494 Epoch 14/100 11610/11610 [==============================] - 0s 43us/sample - loss: 0.3468 - val_loss: 0.3458 Epoch 15/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3417 - val_loss: 0.3487 Epoch 16/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3412 - val_loss: 0.3449 Epoch 17/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3386 - val_loss: 0.3592 Epoch 18/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3372 - val_loss: 0.3412 Epoch 19/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3364 - val_loss: 0.3426 Epoch 20/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3336 - val_loss: 0.3462 Epoch 21/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3317 - val_loss: 0.3388 Epoch 22/100 11610/11610 [==============================] - 0s 43us/sample - loss: 0.3300 - val_loss: 0.3461 Epoch 23/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3292 - val_loss: 0.3355 Epoch 24/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3281 - val_loss: 0.3344 Epoch 25/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3266 - val_loss: 0.3374 Epoch 26/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3283 - val_loss: 0.3348 Epoch 27/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3242 - val_loss: 0.3395 Epoch 28/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3247 - val_loss: 0.3322 Epoch 29/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3233 - val_loss: 0.3288 Epoch 30/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3216 - val_loss: 0.3353 Epoch 31/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3216 - val_loss: 0.3293 Epoch 32/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3214 - val_loss: 0.3312 Epoch 33/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3201 - val_loss: 0.3290 Epoch 34/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3189 - val_loss: 0.3319 5160/1 [==================================================] - 0s 19us/sample - loss: 0.4063 0.342487285580746

这里我们发现，我们设置了100次的迭代，但是只到了34次并没有到100次就停止了，再根据学习曲线的情况，我们发现是EarlyStopping的回调函数起到了作用，是梯度下降已经到了瓶颈，趋于平缓。而测试数据集的损失函数值为0.342。

现在我们来将这个简单的回归模型改成Wide & Deep模型

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import time import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers, models from sklearn.datasets import fetch_california_housing import pprint from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler if __name__ == "__main__": housing = fetch_california_housing() # print(housing.DESCR)  # print(housing.data.shape)  # print(housing.target.shape)  # pprint.pprint(housing.data[0:5])  # pprint.pprint(housing.target[0:5])  X_train_all, X_test, y_train_all, y_test = train_test_split(housing.data, housing.target, random_state=7) X_train, X_valid, y_train, y_valid = train_test_split(X_train_all, y_train_all, random_state=11) # print(X_train.shape, y_train.shape)  # print(X_valid.shape, y_valid.shape)  # print(X_test.shape, y_test.shape)  scaler = StandardScaler() # 归一化  X_train = scaler.fit_transform(X_train) X_valid = scaler.transform(X_valid) X_test = scaler.transform(X_test) # model = keras.models.Sequential([  # layers.Dense(30, activation='relu', input_shape=X_train.shape[1:]),  # layers.Dense(1)  # ])  # 函数式API Deep模型  input = layers.Input(shape=X_train.shape[1:]) hidden1 = layers.Dense(30, activation='relu')(input) hidden2 = layers.Dense(30, activation='relu')(hidden1) # input是Wide模型的输入，hidden2是Deep模型的输出  concat = layers.concatenate([input, hidden2]) output = layers.Dense(1)(concat) model = models.Model(inputs=[input], outputs=[output]) print(model.summary()) # 使用均方误差损失函数和随机梯度下降法  model.compile(loss='mean_squared_error', optimizer=optimizers.SGD(learning_rate=0.001)) callbacks = [keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3)] history = model.fit(X_train, y_train, validation_data=(X_valid, y_valid),  epochs=100, callbacks=callbacks) print(model.evaluate(X_test, y_test)) def plot_learning_curves(history): # 学习曲线  pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history) 

运行结果

 Model: "model" __________________________________________________________________________________________________ Layer (type) Output Shape Param # Connected to ================================================================================================== input_1 (InputLayer) [(None, 8)] 0 __________________________________________________________________________________________________ dense (Dense) (None, 30) 270 input_1[0][0] __________________________________________________________________________________________________ dense_1 (Dense) (None, 30) 930 dense[0][0] __________________________________________________________________________________________________ concatenate (Concatenate) (None, 38) 0 input_1[0][0] dense_1[0][0] __________________________________________________________________________________________________ dense_2 (Dense) (None, 1) 39 concatenate[0][0] ================================================================================================== Total params: 1,239 Trainable params: 1,239 Non-trainable params: 0 __________________________________________________________________________________________________ None Train on 11610 samples, validate on 3870 samples Epoch 1/100 11610/11610 [==============================] - 1s 107us/sample - loss: 1.7756 - val_loss: 0.8341 Epoch 2/100 11610/11610 [==============================] - 1s 56us/sample - loss: 0.7057 - val_loss: 0.7208 Epoch 3/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.6495 - val_loss: 0.6740 Epoch 4/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.6138 - val_loss: 0.6451 Epoch 5/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.5884 - val_loss: 0.6189 Epoch 6/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.5682 - val_loss: 0.6013 Epoch 7/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.5515 - val_loss: 0.5818 Epoch 8/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.5387 - val_loss: 0.5675 Epoch 9/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.5272 - val_loss: 0.5547 Epoch 10/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.5180 - val_loss: 0.5441 Epoch 11/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.5085 - val_loss: 0.5336 Epoch 12/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.5012 - val_loss: 0.5285 Epoch 13/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4931 - val_loss: 0.5167 Epoch 14/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4881 - val_loss: 0.5128 Epoch 15/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4813 - val_loss: 0.5043 Epoch 16/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4760 - val_loss: 0.4983 Epoch 17/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4710 - val_loss: 0.4928 Epoch 18/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4655 - val_loss: 0.4917 Epoch 19/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4621 - val_loss: 0.4818 Epoch 20/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4571 - val_loss: 0.4776 Epoch 21/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4531 - val_loss: 0.4779 Epoch 22/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4501 - val_loss: 0.4696 Epoch 23/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4455 - val_loss: 0.4650 Epoch 24/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4425 - val_loss: 0.4612 Epoch 25/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4404 - val_loss: 0.4592 Epoch 26/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4367 - val_loss: 0.4542 Epoch 27/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4336 - val_loss: 0.4507 Epoch 28/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4310 - val_loss: 0.4492 Epoch 29/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4278 - val_loss: 0.4470 Epoch 30/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4257 - val_loss: 0.4429 Epoch 31/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4227 - val_loss: 0.4398 Epoch 32/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4208 - val_loss: 0.4375 Epoch 33/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4183 - val_loss: 0.4346 Epoch 34/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4162 - val_loss: 0.4327 Epoch 35/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4136 - val_loss: 0.4306 Epoch 36/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4116 - val_loss: 0.4275 Epoch 37/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4096 - val_loss: 0.4258 Epoch 38/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4075 - val_loss: 0.4236 Epoch 39/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4053 - val_loss: 0.4213 Epoch 40/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4037 - val_loss: 0.4191 Epoch 41/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4016 - val_loss: 0.4180 Epoch 42/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.4003 - val_loss: 0.4157 Epoch 43/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3981 - val_loss: 0.4129 Epoch 44/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3962 - val_loss: 0.4130 Epoch 45/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3949 - val_loss: 0.4094 Epoch 46/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3929 - val_loss: 0.4080 Epoch 47/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3915 - val_loss: 0.4067 Epoch 48/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3898 - val_loss: 0.4044 Epoch 49/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3885 - val_loss: 0.4032 Epoch 50/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3868 - val_loss: 0.4019 Epoch 51/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3850 - val_loss: 0.3995 Epoch 52/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3839 - val_loss: 0.3993 Epoch 53/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3825 - val_loss: 0.3971 Epoch 54/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3809 - val_loss: 0.3951 Epoch 55/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3798 - val_loss: 0.3940 Epoch 56/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3788 - val_loss: 0.3929 Epoch 57/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3775 - val_loss: 0.3916 Epoch 58/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3760 - val_loss: 0.3906 Epoch 59/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3749 - val_loss: 0.3900 Epoch 60/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3742 - val_loss: 0.3880 Epoch 61/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3726 - val_loss: 0.3866 Epoch 62/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3718 - val_loss: 0.3863 Epoch 63/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3706 - val_loss: 0.3853 Epoch 64/100 11610/11610 [==============================] - 1s 54us/sample - loss: 0.3698 - val_loss: 0.3834 Epoch 65/100 11610/11610 [==============================] - 1s 71us/sample - loss: 0.3687 - val_loss: 0.3834 Epoch 66/100 11610/11610 [==============================] - 1s 69us/sample - loss: 0.3679 - val_loss: 0.3818 Epoch 67/100 11610/11610 [==============================] - 1s 70us/sample - loss: 0.3668 - val_loss: 0.3811 Epoch 68/100 11610/11610 [==============================] - 1s 78us/sample - loss: 0.3658 - val_loss: 0.3801 Epoch 69/100 11610/11610 [==============================] - 1s 76us/sample - loss: 0.3649 - val_loss: 0.3787 Epoch 70/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.3639 - val_loss: 0.3781 Epoch 71/100 11610/11610 [==============================] - 1s 67us/sample - loss: 0.3634 - val_loss: 0.3769 Epoch 72/100 11610/11610 [==============================] - 1s 67us/sample - loss: 0.3621 - val_loss: 0.3762 Epoch 73/100 11610/11610 [==============================] - 1s 66us/sample - loss: 0.3615 - val_loss: 0.3762 Epoch 74/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3606 - val_loss: 0.3746 Epoch 75/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3596 - val_loss: 0.3749 Epoch 76/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3590 - val_loss: 0.3736 Epoch 77/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3580 - val_loss: 0.3740 Epoch 78/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3576 - val_loss: 0.3721 Epoch 79/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3562 - val_loss: 0.3712 Epoch 80/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3558 - val_loss: 0.3710 Epoch 81/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3549 - val_loss: 0.3710 Epoch 82/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3541 - val_loss: 0.3707 Epoch 83/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3537 - val_loss: 0.3690 Epoch 84/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3530 - val_loss: 0.3691 Epoch 85/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3520 - val_loss: 0.3679 Epoch 86/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3514 - val_loss: 0.3673 Epoch 87/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3508 - val_loss: 0.3671 Epoch 88/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3500 - val_loss: 0.3662 Epoch 89/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3496 - val_loss: 0.3655 Epoch 90/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3487 - val_loss: 0.3661 Epoch 91/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3484 - val_loss: 0.3658 Epoch 92/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3479 - val_loss: 0.3641 Epoch 93/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3468 - val_loss: 0.3637 Epoch 94/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3462 - val_loss: 0.3640 Epoch 95/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3456 - val_loss: 0.3629 Epoch 96/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3449 - val_loss: 0.3621 Epoch 97/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3444 - val_loss: 0.3621 Epoch 98/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3431 - val_loss: 0.3622 Epoch 99/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3434 - val_loss: 0.3606 Epoch 100/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3430 - val_loss: 0.3604 5160/1 [========================================================] - 0s 24us/sample - loss: 0.4557 0.36289026386053985

在这里，我们使用的是函数式编程来实现的Wide & Deep模型，下面我们来使用子类API来实现这个模型

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import time import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers, models from sklearn.datasets import fetch_california_housing import pprint from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler if __name__ == "__main__": housing = fetch_california_housing() # print(housing.DESCR)  # print(housing.data.shape)  # print(housing.target.shape)  # pprint.pprint(housing.data[0:5])  # pprint.pprint(housing.target[0:5])  X_train_all, X_test, y_train_all, y_test = train_test_split(housing.data, housing.target, random_state=7) X_train, X_valid, y_train, y_valid = train_test_split(X_train_all, y_train_all, random_state=11) # print(X_train.shape, y_train.shape)  # print(X_valid.shape, y_valid.shape)  # print(X_test.shape, y_test.shape)  scaler = StandardScaler() # 归一化  X_train = scaler.fit_transform(X_train) X_valid = scaler.transform(X_valid) X_test = scaler.transform(X_test) # model = keras.models.Sequential([  # layers.Dense(30, activation='relu', input_shape=X_train.shape[1:]),  # layers.Dense(1)  # ])  # 函数式API Deep模型  # input = layers.Input(shape=X_train.shape[1:])  # hidden1 = layers.Dense(30, activation='relu')(input)  # hidden2 = layers.Dense(30, activation='relu')(hidden1)  # # input是Wide模型的输入，hidden2是Deep模型的输出  # concat = layers.concatenate([input, hidden2])  # output = layers.Dense(1)(concat)  # model = models.Model(inputs=[input], outputs=[output])  # 子类API，父类为keras.models.Model  class WideDeepModel(models.Model): def __init__(self): super(WideDeepModel, self).__init__() # 定义模型的层次  self.hidden1_layer = layers.Dense(30, activation='relu') self.hidden2_layer = layers.Dense(30, activation='relu') self.output_layer = layers.Dense(1) def call(self, input): # 完成模型的正向计算  hidden1 = self.hidden1_layer(input) hidden2 = self.hidden2_layer(hidden1) concat = layers.concatenate([input, hidden2]) output = self.output_layer(concat) return output model = WideDeepModel() # 也可以使用层堆叠  # model = models.Sequential([  # WideDeepModel()  # ])  model.build(input_shape=(None, 8)) print(model.summary()) # 使用均方误差损失函数和随机梯度下降法  model.compile(loss='mean_squared_error', optimizer=optimizers.SGD(learning_rate=0.001)) callbacks = [keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3)] history = model.fit(X_train, y_train, validation_data=(X_valid, y_valid),  epochs=100, callbacks=callbacks) print(model.evaluate(X_test, y_test)) def plot_learning_curves(history): # 学习曲线  pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history) 

运行结果

 Model: "wide_deep_model" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= dense (Dense) multiple 270 _________________________________________________________________ dense_1 (Dense) multiple 930 _________________________________________________________________ dense_2 (Dense) multiple 39 ================================================================= Total params: 1,239 Trainable params: 1,239 Non-trainable params: 0 _________________________________________________________________ None Train on 11610 samples, validate on 3870 samples Epoch 1/100 11610/11610 [==============================] - 1s 107us/sample - loss: 2.0999 - val_loss: 0.8217 Epoch 2/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.6996 - val_loss: 0.7236 Epoch 3/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.6376 - val_loss: 0.6704 Epoch 4/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.6003 - val_loss: 0.6322 Epoch 5/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.5720 - val_loss: 0.6104 Epoch 6/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.5499 - val_loss: 0.5869 Epoch 7/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.5324 - val_loss: 0.5653 Epoch 8/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.5188 - val_loss: 0.5499 Epoch 9/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.5075 - val_loss: 0.5401 Epoch 10/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.4970 - val_loss: 0.5268 Epoch 11/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.4902 - val_loss: 0.5204 Epoch 12/100 11610/11610 [==============================] - 1s 56us/sample - loss: 0.4819 - val_loss: 0.5103 Epoch 13/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.4759 - val_loss: 0.5056 Epoch 14/100 11610/11610 [==============================] - 1s 82us/sample - loss: 0.4697 - val_loss: 0.4977 Epoch 15/100 11610/11610 [==============================] - 1s 68us/sample - loss: 0.4654 - val_loss: 0.4931 Epoch 16/100 11610/11610 [==============================] - 1s 83us/sample - loss: 0.4597 - val_loss: 0.4928 Epoch 17/100 11610/11610 [==============================] - 1s 78us/sample - loss: 0.4538 - val_loss: 0.4821 Epoch 18/100 11610/11610 [==============================] - 1s 75us/sample - loss: 0.4506 - val_loss: 0.4765 Epoch 19/100 11610/11610 [==============================] - 1s 70us/sample - loss: 0.4465 - val_loss: 0.4744 Epoch 20/100 11610/11610 [==============================] - 1s 58us/sample - loss: 0.4430 - val_loss: 0.4762 Epoch 21/100 11610/11610 [==============================] - 1s 99us/sample - loss: 0.4391 - val_loss: 0.4668 Epoch 22/100 11610/11610 [==============================] - 1s 81us/sample - loss: 0.4361 - val_loss: 0.4641 Epoch 23/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.4328 - val_loss: 0.4587 Epoch 24/100 11610/11610 [==============================] - 1s 66us/sample - loss: 0.4293 - val_loss: 0.4565 Epoch 25/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.4266 - val_loss: 0.4525 Epoch 26/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.4237 - val_loss: 0.4481 Epoch 27/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.4210 - val_loss: 0.4452 Epoch 28/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4178 - val_loss: 0.4426 Epoch 29/100 11610/11610 [==============================] - 1s 75us/sample - loss: 0.4163 - val_loss: 0.4410 Epoch 30/100 11610/11610 [==============================] - 1s 57us/sample - loss: 0.4135 - val_loss: 0.4372 Epoch 31/100 11610/11610 [==============================] - 1s 56us/sample - loss: 0.4111 - val_loss: 0.4350 Epoch 32/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.4096 - val_loss: 0.4329 Epoch 33/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.4075 - val_loss: 0.4298 Epoch 34/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.4053 - val_loss: 0.4293 Epoch 35/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.4035 - val_loss: 0.4263 Epoch 36/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.4018 - val_loss: 0.4236 Epoch 37/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3997 - val_loss: 0.4221 Epoch 38/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3977 - val_loss: 0.4207 Epoch 39/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3962 - val_loss: 0.4175 Epoch 40/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3947 - val_loss: 0.4152 Epoch 41/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3927 - val_loss: 0.4140 Epoch 42/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3914 - val_loss: 0.4131 Epoch 43/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3897 - val_loss: 0.4102 Epoch 44/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3883 - val_loss: 0.4088 Epoch 45/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3869 - val_loss: 0.4063 Epoch 46/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3858 - val_loss: 0.4053 Epoch 47/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3841 - val_loss: 0.4041 Epoch 48/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3832 - val_loss: 0.4029 Epoch 49/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3818 - val_loss: 0.4002 Epoch 50/100 11610/11610 [==============================] - 1s 57us/sample - loss: 0.3807 - val_loss: 0.3987 Epoch 51/100 11610/11610 [==============================] - 1s 77us/sample - loss: 0.3791 - val_loss: 0.3970 Epoch 52/100 11610/11610 [==============================] - 1s 73us/sample - loss: 0.3779 - val_loss: 0.3970 Epoch 53/100 11610/11610 [==============================] - 1s 98us/sample - loss: 0.3768 - val_loss: 0.3964 Epoch 54/100 11610/11610 [==============================] - 1s 92us/sample - loss: 0.3756 - val_loss: 0.3941 Epoch 55/100 11610/11610 [==============================] - 1s 55us/sample - loss: 0.3746 - val_loss: 0.3926 Epoch 56/100 11610/11610 [==============================] - 1s 61us/sample - loss: 0.3739 - val_loss: 0.3914 Epoch 57/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3727 - val_loss: 0.3896 Epoch 58/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3718 - val_loss: 0.3879 Epoch 59/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3701 - val_loss: 0.3900 Epoch 60/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3696 - val_loss: 0.3865 Epoch 61/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3683 - val_loss: 0.3855 Epoch 62/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3674 - val_loss: 0.3860 Epoch 63/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3669 - val_loss: 0.3831 Epoch 64/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3652 - val_loss: 0.3820 Epoch 65/100 11610/11610 [==============================] - 1s 76us/sample - loss: 0.3645 - val_loss: 0.3818 Epoch 66/100 11610/11610 [==============================] - 1s 95us/sample - loss: 0.3641 - val_loss: 0.3794 Epoch 67/100 11610/11610 [==============================] - 1s 82us/sample - loss: 0.3623 - val_loss: 0.3799 Epoch 68/100 11610/11610 [==============================] - 1s 57us/sample - loss: 0.3623 - val_loss: 0.3782 Epoch 69/100 11610/11610 [==============================] - 1s 61us/sample - loss: 0.3606 - val_loss: 0.3766 Epoch 70/100 11610/11610 [==============================] - 1s 68us/sample - loss: 0.3599 - val_loss: 0.3766 Epoch 71/100 11610/11610 [==============================] - 1s 87us/sample - loss: 0.3589 - val_loss: 0.3748 Epoch 72/100 11610/11610 [==============================] - 1s 100us/sample - loss: 0.3582 - val_loss: 0.3743 Epoch 73/100 11610/11610 [==============================] - 1s 60us/sample - loss: 0.3573 - val_loss: 0.3728 Epoch 74/100 11610/11610 [==============================] - 1s 74us/sample - loss: 0.3564 - val_loss: 0.3735 Epoch 75/100 11610/11610 [==============================] - 1s 81us/sample - loss: 0.3562 - val_loss: 0.3718 Epoch 76/100 11610/11610 [==============================] - 1s 75us/sample - loss: 0.3557 - val_loss: 0.3714 Epoch 77/100 11610/11610 [==============================] - 1s 85us/sample - loss: 0.3548 - val_loss: 0.3703 Epoch 78/100 11610/11610 [==============================] - 1s 93us/sample - loss: 0.3540 - val_loss: 0.3700 Epoch 79/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3528 - val_loss: 0.3685 Epoch 80/100 11610/11610 [==============================] - 1s 65us/sample - loss: 0.3526 - val_loss: 0.3678 Epoch 81/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3512 - val_loss: 0.3678 Epoch 82/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3506 - val_loss: 0.3672 Epoch 83/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3508 - val_loss: 0.3657 Epoch 84/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3495 - val_loss: 0.3669 Epoch 85/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3491 - val_loss: 0.3670 Epoch 86/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3490 - val_loss: 0.3642 Epoch 87/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3486 - val_loss: 0.3642 Epoch 88/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3478 - val_loss: 0.3643 Epoch 89/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3474 - val_loss: 0.3631 Epoch 90/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3467 - val_loss: 0.3614 Epoch 91/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3451 - val_loss: 0.3604 Epoch 92/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3444 - val_loss: 0.3606 Epoch 93/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3436 - val_loss: 0.3592 Epoch 94/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3435 - val_loss: 0.3588 Epoch 95/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3424 - val_loss: 0.3585 Epoch 96/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3424 - val_loss: 0.3576 Epoch 97/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3424 - val_loss: 0.3578 Epoch 98/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3419 - val_loss: 0.3569 Epoch 99/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3412 - val_loss: 0.3572 Epoch 100/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3404 - val_loss: 0.3551 5160/1 [===========================================================] - 0s 45us/sample - loss: 0.4603 0.36134041002554484 

由于Wide & Deep模型可以分别挑选特征来进行输入，现在我们来改成多输入的模式

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import time import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers, models from sklearn.datasets import fetch_california_housing import pprint from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler if __name__ == "__main__": housing = fetch_california_housing() # print(housing.DESCR)  # print(housing.data.shape)  # print(housing.target.shape)  # pprint.pprint(housing.data[0:5])  # pprint.pprint(housing.target[0:5])  X_train_all, X_test, y_train_all, y_test = train_test_split(housing.data, housing.target, random_state=7) X_train, X_valid, y_train, y_valid = train_test_split(X_train_all, y_train_all, random_state=11) # print(X_train.shape, y_train.shape)  # print(X_valid.shape, y_valid.shape)  # print(X_test.shape, y_test.shape)  scaler = StandardScaler() # 归一化  X_train = scaler.fit_transform(X_train) X_valid = scaler.transform(X_valid) X_test = scaler.transform(X_test) # model = keras.models.Sequential([  # layers.Dense(30, activation='relu', input_shape=X_train.shape[1:]),  # layers.Dense(1)  # ])  # 函数式API Deep模型  # input = layers.Input(shape=X_train.shape[1:])  # hidden1 = layers.Dense(30, activation='relu')(input)  # hidden2 = layers.Dense(30, activation='relu')(hidden1)  # # input是Wide模型的输入，hidden2是Deep模型的输出  # concat = layers.concatenate([input, hidden2])  # output = layers.Dense(1)(concat)  # model = models.Model(inputs=[input], outputs=[output])  # 子类API，父类为keras.models.Model  # class WideDeepModel(models.Model):  #  # def __init__(self):  # super(WideDeepModel, self).__init__()  # # 定义模型的层次  # self.hidden1_layer = layers.Dense(30, activation='relu')  # self.hidden2_layer = layers.Dense(30, activation='relu')  # self.output_layer = layers.Dense(1)  #  #  # def call(self, input):  # # 完成模型的正向计算  # hidden1 = self.hidden1_layer(input)  # hidden2 = self.hidden2_layer(hidden1)  # concat = layers.concatenate([input, hidden2])  # output = self.output_layer(concat)  # return output  #  # model = WideDeepModel()  # # 也可以使用层堆叠  # # model = models.Sequential([  # # WideDeepModel()  # # ])  # model.build(input_shape=(None, 8))  # 多输入 wide模型输入前5个特征，deep模型输入后6个特征  input_wide = layers.Input(shape=[5]) input_deep = layers.Input(shape=[6]) hidden1 = layers.Dense(30, activation='relu')(input_deep) hidden2 = layers.Dense(30, activation='relu')(hidden1) concat = layers.concatenate([input_wide, hidden2]) output = layers.Dense(1)(concat) model = models.Model(inputs=[input_wide, input_deep], outputs=[output]) print(model.summary()) # 使用均方误差损失函数和随机梯度下降法  model.compile(loss='mean_squared_error', optimizer=optimizers.SGD(learning_rate=0.001)) callbacks = [keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3)] X_train_wide = X_train[:, :5] X_train_deep = X_train[:, 2:] X_valid_wide = X_valid[:, :5] X_valid_deep = X_valid[:, 2:] X_test_wide = X_test[:, :5] X_test_deep = X_test[:, 2:] history = model.fit([X_train_wide, X_train_deep], y_train,  validation_data=([X_valid_wide, X_valid_deep], y_valid),  epochs=100, callbacks=callbacks) print(model.evaluate([X_test_wide, X_test_deep], y_test)) def plot_learning_curves(history): # 学习曲线  pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history) 

运行结果

 Model: "model" __________________________________________________________________________________________________ Layer (type) Output Shape Param # Connected to ================================================================================================== input_2 (InputLayer) [(None, 6)] 0 __________________________________________________________________________________________________ dense (Dense) (None, 30) 210 input_2[0][0] __________________________________________________________________________________________________ input_1 (InputLayer) [(None, 5)] 0 __________________________________________________________________________________________________ dense_1 (Dense) (None, 30) 930 dense[0][0] __________________________________________________________________________________________________ concatenate (Concatenate) (None, 35) 0 input_1[0][0] dense_1[0][0] __________________________________________________________________________________________________ dense_2 (Dense) (None, 1) 36 concatenate[0][0] ================================================================================================== Total params: 1,176 Trainable params: 1,176 Non-trainable params: 0 __________________________________________________________________________________________________ None Train on 11610 samples, validate on 3870 samples Epoch 1/100 11610/11610 [==============================] - 2s 138us/sample - loss: 1.9978 - val_loss: 0.9837 Epoch 2/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.8110 - val_loss: 0.7862 Epoch 3/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.7007 - val_loss: 0.7168 Epoch 4/100 11610/11610 [==============================] - 1s 54us/sample - loss: 0.6489 - val_loss: 0.6742 Epoch 5/100 11610/11610 [==============================] - 1s 54us/sample - loss: 0.6118 - val_loss: 0.6378 Epoch 6/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.5831 - val_loss: 0.6127 Epoch 7/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.5607 - val_loss: 0.5910 Epoch 8/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.5427 - val_loss: 0.5736 Epoch 9/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.5275 - val_loss: 0.5589 Epoch 10/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.5144 - val_loss: 0.5455 Epoch 11/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.5033 - val_loss: 0.5353 Epoch 12/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4939 - val_loss: 0.5258 Epoch 13/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4853 - val_loss: 0.5156 Epoch 14/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4784 - val_loss: 0.5084 Epoch 15/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.4718 - val_loss: 0.5035 Epoch 16/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.4657 - val_loss: 0.4952 Epoch 17/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4606 - val_loss: 0.4887 Epoch 18/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4560 - val_loss: 0.4840 Epoch 19/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4517 - val_loss: 0.4805 Epoch 20/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4477 - val_loss: 0.4773 Epoch 21/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.4451 - val_loss: 0.4727 Epoch 22/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.4423 - val_loss: 0.4697 Epoch 23/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.4397 - val_loss: 0.4708 Epoch 24/100 11610/11610 [==============================] - 1s 72us/sample - loss: 0.4375 - val_loss: 0.4650 Epoch 25/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.4350 - val_loss: 0.4633 Epoch 26/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.4329 - val_loss: 0.4593 Epoch 27/100 11610/11610 [==============================] - 1s 88us/sample - loss: 0.4310 - val_loss: 0.4569 Epoch 28/100 11610/11610 [==============================] - 1s 99us/sample - loss: 0.4294 - val_loss: 0.4558 Epoch 29/100 11610/11610 [==============================] - 1s 97us/sample - loss: 0.4276 - val_loss: 0.4521 Epoch 30/100 11610/11610 [==============================] - 1s 120us/sample - loss: 0.4254 - val_loss: 0.4494 Epoch 31/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.4239 - val_loss: 0.4484 Epoch 32/100 11610/11610 [==============================] - 1s 67us/sample - loss: 0.4219 - val_loss: 0.4470 Epoch 33/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.4209 - val_loss: 0.4456 Epoch 34/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4194 - val_loss: 0.4433 Epoch 35/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4179 - val_loss: 0.4427 Epoch 36/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4163 - val_loss: 0.4399 Epoch 37/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4150 - val_loss: 0.4399 Epoch 38/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4137 - val_loss: 0.4370 Epoch 39/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.4122 - val_loss: 0.4364 Epoch 40/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4112 - val_loss: 0.4369 Epoch 41/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4098 - val_loss: 0.4329 Epoch 42/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4088 - val_loss: 0.4326 Epoch 43/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.4077 - val_loss: 0.4299 Epoch 44/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4066 - val_loss: 0.4304 Epoch 45/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.4054 - val_loss: 0.4284 Epoch 46/100 11610/11610 [==============================] - 1s 84us/sample - loss: 0.4043 - val_loss: 0.4286 Epoch 47/100 11610/11610 [==============================] - 1s 95us/sample - loss: 0.4036 - val_loss: 0.4263 Epoch 48/100 11610/11610 [==============================] - 1s 88us/sample - loss: 0.4026 - val_loss: 0.4251 Epoch 49/100 11610/11610 [==============================] - 1s 82us/sample - loss: 0.4014 - val_loss: 0.4240 Epoch 50/100 11610/11610 [==============================] - 1s 96us/sample - loss: 0.4007 - val_loss: 0.4231 Epoch 51/100 11610/11610 [==============================] - 1s 56us/sample - loss: 0.3998 - val_loss: 0.4216 Epoch 52/100 11610/11610 [==============================] - 1s 67us/sample - loss: 0.3990 - val_loss: 0.4235 Epoch 53/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3981 - val_loss: 0.4211 Epoch 54/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3976 - val_loss: 0.4210 Epoch 55/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3965 - val_loss: 0.4217 Epoch 56/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3959 - val_loss: 0.4174 Epoch 57/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3953 - val_loss: 0.4175 Epoch 58/100 11610/11610 [==============================] - 1s 82us/sample - loss: 0.3943 - val_loss: 0.4163 Epoch 59/100 11610/11610 [==============================] - 1s 74us/sample - loss: 0.3935 - val_loss: 0.4156 Epoch 60/100 11610/11610 [==============================] - 1s 77us/sample - loss: 0.3928 - val_loss: 0.4150 Epoch 61/100 11610/11610 [==============================] - 1s 70us/sample - loss: 0.3922 - val_loss: 0.4147 Epoch 62/100 11610/11610 [==============================] - 1s 55us/sample - loss: 0.3913 - val_loss: 0.4137 Epoch 63/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.3906 - val_loss: 0.4128 Epoch 64/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3898 - val_loss: 0.4113 Epoch 65/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3894 - val_loss: 0.4121 Epoch 66/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3884 - val_loss: 0.4110 Epoch 67/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3878 - val_loss: 0.4129 Epoch 68/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3873 - val_loss: 0.4109 Epoch 69/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3864 - val_loss: 0.4101 Epoch 70/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3858 - val_loss: 0.4092 Epoch 71/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3853 - val_loss: 0.4073 Epoch 72/100 11610/11610 [==============================] - 1s 94us/sample - loss: 0.3847 - val_loss: 0.4076 Epoch 73/100 11610/11610 [==============================] - 1s 98us/sample - loss: 0.3842 - val_loss: 0.4059 Epoch 74/100 11610/11610 [==============================] - 1s 80us/sample - loss: 0.3834 - val_loss: 0.4047 Epoch 75/100 11610/11610 [==============================] - 1s 65us/sample - loss: 0.3826 - val_loss: 0.4056 Epoch 76/100 11610/11610 [==============================] - 1s 64us/sample - loss: 0.3822 - val_loss: 0.4031 Epoch 77/100 11610/11610 [==============================] - 1s 67us/sample - loss: 0.3814 - val_loss: 0.4049 Epoch 78/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3812 - val_loss: 0.4029 Epoch 79/100 11610/11610 [==============================] - 1s 59us/sample - loss: 0.3800 - val_loss: 0.4022 Epoch 80/100 11610/11610 [==============================] - 1s 65us/sample - loss: 0.3794 - val_loss: 0.4004 Epoch 81/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3793 - val_loss: 0.4004 Epoch 82/100 11610/11610 [==============================] - 1s 79us/sample - loss: 0.3784 - val_loss: 0.3998 Epoch 83/100 11610/11610 [==============================] - 1s 77us/sample - loss: 0.3778 - val_loss: 0.3988 Epoch 84/100 11610/11610 [==============================] - 1s 65us/sample - loss: 0.3770 - val_loss: 0.3981 Epoch 85/100 11610/11610 [==============================] - 1s 69us/sample - loss: 0.3764 - val_loss: 0.3987 Epoch 86/100 11610/11610 [==============================] - 1s 83us/sample - loss: 0.3756 - val_loss: 0.3970 Epoch 87/100 11610/11610 [==============================] - 1s 89us/sample - loss: 0.3751 - val_loss: 0.3969 Epoch 88/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.3747 - val_loss: 0.3950 Epoch 89/100 11610/11610 [==============================] - 1s 90us/sample - loss: 0.3740 - val_loss: 0.3951 Epoch 90/100 11610/11610 [==============================] - 1s 68us/sample - loss: 0.3733 - val_loss: 0.3945 Epoch 91/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3727 - val_loss: 0.3937 Epoch 92/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3721 - val_loss: 0.3937 Epoch 93/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3717 - val_loss: 0.3932 Epoch 94/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3709 - val_loss: 0.3930 Epoch 95/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3703 - val_loss: 0.3919 Epoch 96/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3695 - val_loss: 0.3921 Epoch 97/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3692 - val_loss: 0.3909 Epoch 98/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3687 - val_loss: 0.3892 Epoch 99/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3676 - val_loss: 0.3902 Epoch 100/100 11610/11610 [==============================] - 1s 53us/sample - loss: 0.3677 - val_loss: 0.3888 5160/1 [=======================================================] - 0s 24us/sample - loss: 0.4975 0.3788368522658829

有了多输入就会有多输出

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import time import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers, models from sklearn.datasets import fetch_california_housing import pprint from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler if __name__ == "__main__": housing = fetch_california_housing() # print(housing.DESCR)  # print(housing.data.shape)  # print(housing.target.shape)  # pprint.pprint(housing.data[0:5])  # pprint.pprint(housing.target[0:5])  X_train_all, X_test, y_train_all, y_test = train_test_split(housing.data, housing.target, random_state=7) X_train, X_valid, y_train, y_valid = train_test_split(X_train_all, y_train_all, random_state=11) # print(X_train.shape, y_train.shape)  # print(X_valid.shape, y_valid.shape)  # print(X_test.shape, y_test.shape)  scaler = StandardScaler() # 归一化  X_train = scaler.fit_transform(X_train) X_valid = scaler.transform(X_valid) X_test = scaler.transform(X_test) # model = keras.models.Sequential([  # layers.Dense(30, activation='relu', input_shape=X_train.shape[1:]),  # layers.Dense(1)  # ])  # 函数式API Deep模型  # input = layers.Input(shape=X_train.shape[1:])  # hidden1 = layers.Dense(30, activation='relu')(input)  # hidden2 = layers.Dense(30, activation='relu')(hidden1)  # # input是Wide模型的输入，hidden2是Deep模型的输出  # concat = layers.concatenate([input, hidden2])  # output = layers.Dense(1)(concat)  # model = models.Model(inputs=[input], outputs=[output])  # 子类API，父类为keras.models.Model  # class WideDeepModel(models.Model):  #  # def __init__(self):  # super(WideDeepModel, self).__init__()  # # 定义模型的层次  # self.hidden1_layer = layers.Dense(30, activation='relu')  # self.hidden2_layer = layers.Dense(30, activation='relu')  # self.output_layer = layers.Dense(1)  #  #  # def call(self, input):  # # 完成模型的正向计算  # hidden1 = self.hidden1_layer(input)  # hidden2 = self.hidden2_layer(hidden1)  # concat = layers.concatenate([input, hidden2])  # output = self.output_layer(concat)  # return output  #  # model = WideDeepModel()  # # 也可以使用层堆叠  # # model = models.Sequential([  # # WideDeepModel()  # # ])  # model.build(input_shape=(None, 8))  # 多输入 wide模型输入前5个特征，deep模型输入后6个特征  input_wide = layers.Input(shape=[5]) input_deep = layers.Input(shape=[6]) hidden1 = layers.Dense(30, activation='relu')(input_deep) hidden2 = layers.Dense(30, activation='relu')(hidden1) concat = layers.concatenate([input_wide, hidden2]) # 多输出  output1 = layers.Dense(1)(concat) output2 = layers.Dense(1)(hidden2) model = models.Model(inputs=[input_wide, input_deep], outputs=[output1, output2]) print(model.summary()) # 使用均方误差损失函数和随机梯度下降法  model.compile(loss='mean_squared_error', optimizer=optimizers.SGD(learning_rate=0.001)) callbacks = [keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3)] X_train_wide = X_train[:, :5] X_train_deep = X_train[:, 2:] X_valid_wide = X_valid[:, :5] X_valid_deep = X_valid[:, 2:] X_test_wide = X_test[:, :5] X_test_deep = X_test[:, 2:] history = model.fit([X_train_wide, X_train_deep], [y_train, y_train],  validation_data=([X_valid_wide, X_valid_deep], [y_valid, y_valid]),  epochs=100, callbacks=callbacks) print(model.evaluate([X_test_wide, X_test_deep], [y_test, y_test])) def plot_learning_curves(history): # 学习曲线  pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history) 

运行结果

 Model: "model" __________________________________________________________________________________________________ Layer (type) Output Shape Param # Connected to ================================================================================================== input_2 (InputLayer) [(None, 6)] 0 __________________________________________________________________________________________________ dense (Dense) (None, 30) 210 input_2[0][0] __________________________________________________________________________________________________ input_1 (InputLayer) [(None, 5)] 0 __________________________________________________________________________________________________ dense_1 (Dense) (None, 30) 930 dense[0][0] __________________________________________________________________________________________________ concatenate (Concatenate) (None, 35) 0 input_1[0][0] dense_1[0][0] __________________________________________________________________________________________________ dense_2 (Dense) (None, 1) 36 concatenate[0][0] __________________________________________________________________________________________________ dense_3 (Dense) (None, 1) 31 dense_1[0][0] ================================================================================================== Total params: 1,207 Trainable params: 1,207 Non-trainable params: 0 __________________________________________________________________________________________________ None Train on 11610 samples, validate on 3870 samples Epoch 1/100 11610/11610 [==============================] - 2s 151us/sample - loss: 4.6904 - dense_2_loss: 2.2887 - dense_3_loss: 2.4007 - val_loss: 2.2365 - val_dense_2_loss: 0.8763 - val_dense_3_loss: 1.3602 Epoch 2/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.8804 - dense_2_loss: 0.7132 - dense_3_loss: 1.1668 - val_loss: 1.8578 - val_dense_2_loss: 0.6893 - val_dense_3_loss: 1.1685 Epoch 3/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.6375 - dense_2_loss: 0.6051 - dense_3_loss: 1.0320 - val_loss: 1.6503 - val_dense_2_loss: 0.6125 - val_dense_3_loss: 1.0377 Epoch 4/100 11610/11610 [==============================] - 1s 63us/sample - loss: 1.4545 - dense_2_loss: 0.5502 - dense_3_loss: 0.9039 - val_loss: 1.4679 - val_dense_2_loss: 0.5670 - val_dense_3_loss: 0.9009 Epoch 5/100 11610/11610 [==============================] - 1s 61us/sample - loss: 1.3185 - dense_2_loss: 0.5166 - dense_3_loss: 0.8021 - val_loss: 1.3543 - val_dense_2_loss: 0.5365 - val_dense_3_loss: 0.8177 Epoch 6/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.2300 - dense_2_loss: 0.4951 - dense_3_loss: 0.7349 - val_loss: 1.2700 - val_dense_2_loss: 0.5162 - val_dense_3_loss: 0.7536 Epoch 7/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.1740 - dense_2_loss: 0.4805 - dense_3_loss: 0.6936 - val_loss: 1.2194 - val_dense_2_loss: 0.5032 - val_dense_3_loss: 0.7161 Epoch 8/100 11610/11610 [==============================] - 1s 61us/sample - loss: 1.1349 - dense_2_loss: 0.4695 - dense_3_loss: 0.6651 - val_loss: 1.1812 - val_dense_2_loss: 0.4888 - val_dense_3_loss: 0.6923 Epoch 9/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.1066 - dense_2_loss: 0.4612 - dense_3_loss: 0.6452 - val_loss: 1.1580 - val_dense_2_loss: 0.4876 - val_dense_3_loss: 0.6703 Epoch 10/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.0847 - dense_2_loss: 0.4549 - dense_3_loss: 0.6300 - val_loss: 1.1370 - val_dense_2_loss: 0.4784 - val_dense_3_loss: 0.6585 Epoch 11/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.0667 - dense_2_loss: 0.4483 - dense_3_loss: 0.6183 - val_loss: 1.1159 - val_dense_2_loss: 0.4717 - val_dense_3_loss: 0.6441 Epoch 12/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.0524 - dense_2_loss: 0.4440 - dense_3_loss: 0.6086 - val_loss: 1.1014 - val_dense_2_loss: 0.4640 - val_dense_3_loss: 0.6373 Epoch 13/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.0388 - dense_2_loss: 0.4397 - dense_3_loss: 0.5995 - val_loss: 1.0919 - val_dense_2_loss: 0.4677 - val_dense_3_loss: 0.6241 Epoch 14/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.0277 - dense_2_loss: 0.4357 - dense_3_loss: 0.5921 - val_loss: 1.0758 - val_dense_2_loss: 0.4573 - val_dense_3_loss: 0.6184 Epoch 15/100 11610/11610 [==============================] - 1s 61us/sample - loss: 1.0185 - dense_2_loss: 0.4323 - dense_3_loss: 0.5861 - val_loss: 1.0668 - val_dense_2_loss: 0.4580 - val_dense_3_loss: 0.6087 Epoch 16/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.0102 - dense_2_loss: 0.4295 - dense_3_loss: 0.5807 - val_loss: 1.0546 - val_dense_2_loss: 0.4518 - val_dense_3_loss: 0.6027 Epoch 17/100 11610/11610 [==============================] - 1s 62us/sample - loss: 1.0019 - dense_2_loss: 0.4267 - dense_3_loss: 0.5751 - val_loss: 1.0487 - val_dense_2_loss: 0.4512 - val_dense_3_loss: 0.5974 Epoch 18/100 11610/11610 [==============================] - 1s 84us/sample - loss: 0.9950 - dense_2_loss: 0.4239 - dense_3_loss: 0.5714 - val_loss: 1.0379 - val_dense_2_loss: 0.4465 - val_dense_3_loss: 0.5913 Epoch 19/100 11610/11610 [==============================] - 1s 109us/sample - loss: 0.9884 - dense_2_loss: 0.4213 - dense_3_loss: 0.5668 - val_loss: 1.0312 - val_dense_2_loss: 0.4447 - val_dense_3_loss: 0.5864 Epoch 20/100 11610/11610 [==============================] - 1s 82us/sample - loss: 0.9820 - dense_2_loss: 0.4188 - dense_3_loss: 0.5630 - val_loss: 1.0274 - val_dense_2_loss: 0.4428 - val_dense_3_loss: 0.5844 Epoch 21/100 11610/11610 [==============================] - 1s 68us/sample - loss: 0.9757 - dense_2_loss: 0.4165 - dense_3_loss: 0.5590 - val_loss: 1.0197 - val_dense_2_loss: 0.4413 - val_dense_3_loss: 0.5783 Epoch 22/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.9690 - dense_2_loss: 0.4140 - dense_3_loss: 0.5547 - val_loss: 1.0125 - val_dense_2_loss: 0.4372 - val_dense_3_loss: 0.5752 Epoch 23/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9633 - dense_2_loss: 0.4119 - dense_3_loss: 0.5514 - val_loss: 1.0073 - val_dense_2_loss: 0.4348 - val_dense_3_loss: 0.5723 Epoch 24/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9581 - dense_2_loss: 0.4105 - dense_3_loss: 0.5483 - val_loss: 1.0053 - val_dense_2_loss: 0.4386 - val_dense_3_loss: 0.5666 Epoch 25/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9543 - dense_2_loss: 0.4085 - dense_3_loss: 0.5457 - val_loss: 0.9971 - val_dense_2_loss: 0.4320 - val_dense_3_loss: 0.5650 Epoch 26/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9473 - dense_2_loss: 0.4054 - dense_3_loss: 0.5417 - val_loss: 0.9948 - val_dense_2_loss: 0.4335 - val_dense_3_loss: 0.5612 Epoch 27/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9427 - dense_2_loss: 0.4044 - dense_3_loss: 0.5383 - val_loss: 0.9884 - val_dense_2_loss: 0.4279 - val_dense_3_loss: 0.5604 Epoch 28/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9392 - dense_2_loss: 0.4028 - dense_3_loss: 0.5362 - val_loss: 0.9836 - val_dense_2_loss: 0.4280 - val_dense_3_loss: 0.5555 Epoch 29/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9333 - dense_2_loss: 0.4003 - dense_3_loss: 0.5329 - val_loss: 0.9803 - val_dense_2_loss: 0.4257 - val_dense_3_loss: 0.5544 Epoch 30/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9297 - dense_2_loss: 0.3990 - dense_3_loss: 0.5304 - val_loss: 0.9735 - val_dense_2_loss: 0.4229 - val_dense_3_loss: 0.5505 Epoch 31/100 11610/11610 [==============================] - 1s 64us/sample - loss: 0.9257 - dense_2_loss: 0.3978 - dense_3_loss: 0.5278 - val_loss: 0.9735 - val_dense_2_loss: 0.4216 - val_dense_3_loss: 0.5518 Epoch 32/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9202 - dense_2_loss: 0.3956 - dense_3_loss: 0.5247 - val_loss: 0.9665 - val_dense_2_loss: 0.4209 - val_dense_3_loss: 0.5455 Epoch 33/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9178 - dense_2_loss: 0.3946 - dense_3_loss: 0.5229 - val_loss: 0.9594 - val_dense_2_loss: 0.4180 - val_dense_3_loss: 0.5413 Epoch 34/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9121 - dense_2_loss: 0.3925 - dense_3_loss: 0.5197 - val_loss: 0.9559 - val_dense_2_loss: 0.4147 - val_dense_3_loss: 0.5411 Epoch 35/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9080 - dense_2_loss: 0.3910 - dense_3_loss: 0.5168 - val_loss: 0.9536 - val_dense_2_loss: 0.4119 - val_dense_3_loss: 0.5415 Epoch 36/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9046 - dense_2_loss: 0.3900 - dense_3_loss: 0.5146 - val_loss: 0.9511 - val_dense_2_loss: 0.4139 - val_dense_3_loss: 0.5371 Epoch 37/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.9000 - dense_2_loss: 0.3882 - dense_3_loss: 0.5118 - val_loss: 0.9507 - val_dense_2_loss: 0.4199 - val_dense_3_loss: 0.5307 Epoch 38/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8990 - dense_2_loss: 0.3884 - dense_3_loss: 0.5110 - val_loss: 0.9416 - val_dense_2_loss: 0.4145 - val_dense_3_loss: 0.5270 Epoch 39/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8928 - dense_2_loss: 0.3859 - dense_3_loss: 0.5071 - val_loss: 0.9357 - val_dense_2_loss: 0.4092 - val_dense_3_loss: 0.5264 Epoch 40/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8882 - dense_2_loss: 0.3838 - dense_3_loss: 0.5044 - val_loss: 0.9325 - val_dense_2_loss: 0.4092 - val_dense_3_loss: 0.5233 Epoch 41/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8846 - dense_2_loss: 0.3831 - dense_3_loss: 0.5016 - val_loss: 0.9277 - val_dense_2_loss: 0.4055 - val_dense_3_loss: 0.5221 Epoch 42/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8831 - dense_2_loss: 0.3827 - dense_3_loss: 0.5002 - val_loss: 0.9259 - val_dense_2_loss: 0.4053 - val_dense_3_loss: 0.5205 Epoch 43/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8804 - dense_2_loss: 0.3817 - dense_3_loss: 0.4987 - val_loss: 0.9199 - val_dense_2_loss: 0.4035 - val_dense_3_loss: 0.5163 Epoch 44/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8737 - dense_2_loss: 0.3792 - dense_3_loss: 0.4946 - val_loss: 0.9165 - val_dense_2_loss: 0.4009 - val_dense_3_loss: 0.5154 Epoch 45/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8698 - dense_2_loss: 0.3776 - dense_3_loss: 0.4920 - val_loss: 0.9099 - val_dense_2_loss: 0.3978 - val_dense_3_loss: 0.5120 Epoch 46/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8689 - dense_2_loss: 0.3779 - dense_3_loss: 0.4910 - val_loss: 0.9068 - val_dense_2_loss: 0.3983 - val_dense_3_loss: 0.5084 Epoch 47/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8622 - dense_2_loss: 0.3751 - dense_3_loss: 0.4870 - val_loss: 0.9008 - val_dense_2_loss: 0.3938 - val_dense_3_loss: 0.5069 Epoch 48/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8588 - dense_2_loss: 0.3739 - dense_3_loss: 0.4848 - val_loss: 0.8974 - val_dense_2_loss: 0.3932 - val_dense_3_loss: 0.5041 Epoch 49/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8582 - dense_2_loss: 0.3740 - dense_3_loss: 0.4840 - val_loss: 0.8923 - val_dense_2_loss: 0.3919 - val_dense_3_loss: 0.5003 Epoch 50/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8522 - dense_2_loss: 0.3718 - dense_3_loss: 0.4803 - val_loss: 0.8924 - val_dense_2_loss: 0.3922 - val_dense_3_loss: 0.5000 Epoch 51/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.8503 - dense_2_loss: 0.3715 - dense_3_loss: 0.4789 - val_loss: 0.8888 - val_dense_2_loss: 0.3900 - val_dense_3_loss: 0.4986 Epoch 52/100 11610/11610 [==============================] - 1s 61us/sample - loss: 0.8487 - dense_2_loss: 0.3714 - dense_3_loss: 0.4772 - val_loss: 0.8834 - val_dense_2_loss: 0.3910 - val_dense_3_loss: 0.4923 Epoch 53/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8443 - dense_2_loss: 0.3696 - dense_3_loss: 0.4746 - val_loss: 0.8799 - val_dense_2_loss: 0.3882 - val_dense_3_loss: 0.4915 Epoch 54/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8423 - dense_2_loss: 0.3691 - dense_3_loss: 0.4731 - val_loss: 0.8745 - val_dense_2_loss: 0.3870 - val_dense_3_loss: 0.4874 Epoch 55/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8385 - dense_2_loss: 0.3679 - dense_3_loss: 0.4705 - val_loss: 0.8729 - val_dense_2_loss: 0.3859 - val_dense_3_loss: 0.4870 Epoch 56/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8307 - dense_2_loss: 0.3647 - dense_3_loss: 0.4659 - val_loss: 0.8685 - val_dense_2_loss: 0.3823 - val_dense_3_loss: 0.4861 Epoch 57/100 11610/11610 [==============================] - 1s 64us/sample - loss: 0.8316 - dense_2_loss: 0.3654 - dense_3_loss: 0.4663 - val_loss: 0.8642 - val_dense_2_loss: 0.3818 - val_dense_3_loss: 0.4823 Epoch 58/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8277 - dense_2_loss: 0.3640 - dense_3_loss: 0.4636 - val_loss: 0.8592 - val_dense_2_loss: 0.3810 - val_dense_3_loss: 0.4781 Epoch 59/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8323 - dense_2_loss: 0.3661 - dense_3_loss: 0.4661 - val_loss: 0.8578 - val_dense_2_loss: 0.3809 - val_dense_3_loss: 0.4768 Epoch 60/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8185 - dense_2_loss: 0.3608 - dense_3_loss: 0.4580 - val_loss: 0.8512 - val_dense_2_loss: 0.3777 - val_dense_3_loss: 0.4734 Epoch 61/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8188 - dense_2_loss: 0.3609 - dense_3_loss: 0.4577 - val_loss: 0.8514 - val_dense_2_loss: 0.3779 - val_dense_3_loss: 0.4734 Epoch 62/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8165 - dense_2_loss: 0.3608 - dense_3_loss: 0.4556 - val_loss: 0.8442 - val_dense_2_loss: 0.3746 - val_dense_3_loss: 0.4695 Epoch 63/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.8118 - dense_2_loss: 0.3589 - dense_3_loss: 0.4530 - val_loss: 0.8407 - val_dense_2_loss: 0.3724 - val_dense_3_loss: 0.4682 Epoch 64/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8097 - dense_2_loss: 0.3587 - dense_3_loss: 0.4512 - val_loss: 0.8400 - val_dense_2_loss: 0.3758 - val_dense_3_loss: 0.4640 Epoch 65/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8025 - dense_2_loss: 0.3552 - dense_3_loss: 0.4471 - val_loss: 0.8353 - val_dense_2_loss: 0.3721 - val_dense_3_loss: 0.4631 Epoch 66/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7997 - dense_2_loss: 0.3542 - dense_3_loss: 0.4456 - val_loss: 0.8299 - val_dense_2_loss: 0.3707 - val_dense_3_loss: 0.4591 Epoch 67/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.8013 - dense_2_loss: 0.3553 - dense_3_loss: 0.4458 - val_loss: 0.8289 - val_dense_2_loss: 0.3691 - val_dense_3_loss: 0.4597 Epoch 68/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7985 - dense_2_loss: 0.3548 - dense_3_loss: 0.4436 - val_loss: 0.8209 - val_dense_2_loss: 0.3677 - val_dense_3_loss: 0.4532 Epoch 69/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7968 - dense_2_loss: 0.3538 - dense_3_loss: 0.4428 - val_loss: 0.8211 - val_dense_2_loss: 0.3682 - val_dense_3_loss: 0.4527 Epoch 70/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7889 - dense_2_loss: 0.3510 - dense_3_loss: 0.4378 - val_loss: 0.8174 - val_dense_2_loss: 0.3667 - val_dense_3_loss: 0.4506 Epoch 71/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7877 - dense_2_loss: 0.3506 - dense_3_loss: 0.4373 - val_loss: 0.8115 - val_dense_2_loss: 0.3632 - val_dense_3_loss: 0.4482 Epoch 72/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7845 - dense_2_loss: 0.3496 - dense_3_loss: 0.4354 - val_loss: 0.8157 - val_dense_2_loss: 0.3665 - val_dense_3_loss: 0.4490 Epoch 73/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7818 - dense_2_loss: 0.3487 - dense_3_loss: 0.4332 - val_loss: 0.8084 - val_dense_2_loss: 0.3622 - val_dense_3_loss: 0.4461 Epoch 74/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.7843 - dense_2_loss: 0.3501 - dense_3_loss: 0.4348 - val_loss: 0.8084 - val_dense_2_loss: 0.3620 - val_dense_3_loss: 0.4463 Epoch 75/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7785 - dense_2_loss: 0.3474 - dense_3_loss: 0.4311 - val_loss: 0.8079 - val_dense_2_loss: 0.3622 - val_dense_3_loss: 0.4457 Epoch 76/100 11610/11610 [==============================] - 1s 61us/sample - loss: 0.7765 - dense_2_loss: 0.3470 - dense_3_loss: 0.4295 - val_loss: 0.8049 - val_dense_2_loss: 0.3639 - val_dense_3_loss: 0.4409 Epoch 77/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7735 - dense_2_loss: 0.3460 - dense_3_loss: 0.4276 - val_loss: 0.8012 - val_dense_2_loss: 0.3612 - val_dense_3_loss: 0.4399 Epoch 78/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7730 - dense_2_loss: 0.3459 - dense_3_loss: 0.4273 - val_loss: 0.8023 - val_dense_2_loss: 0.3603 - val_dense_3_loss: 0.4419 Epoch 79/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7756 - dense_2_loss: 0.3472 - dense_3_loss: 0.4284 - val_loss: 0.7986 - val_dense_2_loss: 0.3576 - val_dense_3_loss: 0.4409 Epoch 80/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7761 - dense_2_loss: 0.3475 - dense_3_loss: 0.4286 - val_loss: 0.7979 - val_dense_2_loss: 0.3598 - val_dense_3_loss: 0.4380 Epoch 81/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7733 - dense_2_loss: 0.3466 - dense_3_loss: 0.4267 - val_loss: 0.7936 - val_dense_2_loss: 0.3593 - val_dense_3_loss: 0.4341 Epoch 82/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7655 - dense_2_loss: 0.3430 - dense_3_loss: 0.4224 - val_loss: 0.7945 - val_dense_2_loss: 0.3580 - val_dense_3_loss: 0.4363 Epoch 83/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7669 - dense_2_loss: 0.3442 - dense_3_loss: 0.4224 - val_loss: 0.7913 - val_dense_2_loss: 0.3572 - val_dense_3_loss: 0.4340 Epoch 84/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7617 - dense_2_loss: 0.3424 - dense_3_loss: 0.4194 - val_loss: 0.7889 - val_dense_2_loss: 0.3561 - val_dense_3_loss: 0.4326 Epoch 85/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7601 - dense_2_loss: 0.3414 - dense_3_loss: 0.4186 - val_loss: 0.7866 - val_dense_2_loss: 0.3560 - val_dense_3_loss: 0.4304 Epoch 86/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7578 - dense_2_loss: 0.3408 - dense_3_loss: 0.4169 - val_loss: 0.7873 - val_dense_2_loss: 0.3562 - val_dense_3_loss: 0.4309 Epoch 87/100 11610/11610 [==============================] - 1s 61us/sample - loss: 0.7631 - dense_2_loss: 0.3432 - dense_3_loss: 0.4198 - val_loss: 0.7842 - val_dense_2_loss: 0.3540 - val_dense_3_loss: 0.4302 Epoch 88/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7603 - dense_2_loss: 0.3422 - dense_3_loss: 0.4181 - val_loss: 0.7832 - val_dense_2_loss: 0.3549 - val_dense_3_loss: 0.4282 Epoch 89/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7542 - dense_2_loss: 0.3391 - dense_3_loss: 0.4148 - val_loss: 0.7893 - val_dense_2_loss: 0.3571 - val_dense_3_loss: 0.4320 Epoch 90/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7528 - dense_2_loss: 0.3391 - dense_3_loss: 0.4139 - val_loss: 0.7808 - val_dense_2_loss: 0.3533 - val_dense_3_loss: 0.4274 Epoch 91/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7523 - dense_2_loss: 0.3385 - dense_3_loss: 0.4137 - val_loss: 0.7778 - val_dense_2_loss: 0.3532 - val_dense_3_loss: 0.4245 Epoch 92/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7514 - dense_2_loss: 0.3390 - dense_3_loss: 0.4130 - val_loss: 0.7748 - val_dense_2_loss: 0.3507 - val_dense_3_loss: 0.4241 Epoch 93/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.7479 - dense_2_loss: 0.3371 - dense_3_loss: 0.4106 - val_loss: 0.7771 - val_dense_2_loss: 0.3529 - val_dense_3_loss: 0.4241 Epoch 94/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7477 - dense_2_loss: 0.3371 - dense_3_loss: 0.4105 - val_loss: 0.7711 - val_dense_2_loss: 0.3500 - val_dense_3_loss: 0.4210 Epoch 95/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7519 - dense_2_loss: 0.3391 - dense_3_loss: 0.4126 - val_loss: 0.7720 - val_dense_2_loss: 0.3507 - val_dense_3_loss: 0.4212 Epoch 96/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.7544 - dense_2_loss: 0.3404 - dense_3_loss: 0.4140 - val_loss: 0.7853 - val_dense_2_loss: 0.3559 - val_dense_3_loss: 0.4293 Epoch 97/100 11610/11610 [==============================] - 1s 81us/sample - loss: 0.7543 - dense_2_loss: 0.3404 - dense_3_loss: 0.4140 - val_loss: 0.7712 - val_dense_2_loss: 0.3506 - val_dense_3_loss: 0.4205 Epoch 98/100 11610/11610 [==============================] - 1s 95us/sample - loss: 0.7540 - dense_2_loss: 0.3405 - dense_3_loss: 0.4140 - val_loss: 0.7728 - val_dense_2_loss: 0.3520 - val_dense_3_loss: 0.4207 Epoch 99/100 11610/11610 [==============================] - 1s 64us/sample - loss: 0.7424 - dense_2_loss: 0.3352 - dense_3_loss: 0.4070 - val_loss: 0.7710 - val_dense_2_loss: 0.3507 - val_dense_3_loss: 0.4203 5160/1 [====================================================] - 0s 29us/sample - loss: 0.8831 - dense_2_loss: 0.3513 - dense_3_loss: 0.4160 [0.7661929805149403, 0.35130394, 0.41597202]

这里会有三组线，一个是总的，一个是第一个输出，一个是第二个输出。

基础API

我们现在来看一下tensorflow中最基本的常量操作

 import tensorflow as tf import numpy as np if __name__ == "__main__": # 定义矩阵常量  t = tf.constant([[1., 2., 3.], [4., 5., 6.]]) print(t) print(t[:, 1:]) print(t[:, 1]) # 算子  print(t + 10) # 计算平方  print(tf.square(t)) # 计算它本身和它转置的点乘  print(t @ tf.transpose(t)) # 获取numpy的值  print(t.numpy()) # 作为numpy的输入  print(np.square(t)) # 将numpy对象转成tensorflow对象  np_t = np.array([[1., 2., 3.], [4., 5., 6.]]) print(tf.constant(np_t)) # 标量  num = tf.constant(2.718) print(num) print(num.numpy()) print(num.shape) # 字符串  t = tf.constant("coffee") print(t) print(tf.strings.length(t)) print(tf.strings.length(t, unit='UTF8_CHAR')) # 解码成utf8编码  print(tf.strings.unicode_decode(t, 'UTF8')) # 字符串数组  t = tf.constant(['cafe', 'coffee', '咖啡']) print(t) print(tf.strings.length(t, unit='UTF8_CHAR')) print(tf.strings.unicode_decode(t, 'UTF8')) # ragged tensor不等长的数组  r = tf.ragged.constant([[11, 12], [21, 22, 23], [], [41]]) print(r) print(r[1]) print(r[1:3]) # ragged tensor算子  r2 = tf.ragged.constant([[51, 52], [], [71], [42, 43]]) # 在第0个维度上进行拼接  print(tf.concat([r, r2], axis=0)) # 在第1个维度上进行拼接,如果第一个维度的数量不相等，会报错  print(tf.concat([r, r2], axis=1)) # 将ragged tensor转化为普通tensor，空缺位置补0  print(r.to_tensor()) # sparse tensor 大部分位置的值为0，只有少部分不为0  # indices必须排序放置，否则转普通tensor会报错  s = tf.SparseTensor(indices=[[0, 1], [1, 0], [2, 3]],  values=[1., 2., 3], dense_shape=[3, 4]) print(s) # 将sparse tensor转化为普通的tensor  print(tf.sparse.to_dense(s)) # sparse tensor算子  s2 = s * 2.0  print(s2) try: s3 = s + 1.  except TypeError as ex: print(ex) s4 = tf.constant([[10., 20.], [30., 40.], [50., 60.], [70., 80.]]) # 矩阵乘法  print(tf.sparse.sparse_dense_matmul(s, s4)) s5 = tf.SparseTensor(indices=[[0, 2], [0, 1], [2, 3]],  values=[1., 2., 3], dense_shape=[3, 4]) print(s5) try: print(tf.sparse.to_dense(s5)) except Exception as ex: print(ex) s6 = tf.sparse.reorder(s5) print(tf.sparse.to_dense(s6))

运行结果

 tf.Tensor( [[1. 2. 3.] [4. 5. 6.]], shape=(2, 3), dtype=float32) tf.Tensor( [[2. 3.] [5. 6.]], shape=(2, 2), dtype=float32) tf.Tensor([2. 5.], shape=(2,), dtype=float32) tf.Tensor( [[11. 12. 13.] [14. 15. 16.]], shape=(2, 3), dtype=float32) tf.Tensor( [[ 1. 4. 9.] [16. 25. 36.]], shape=(2, 3), dtype=float32) tf.Tensor( [[14. 32.] [32. 77.]], shape=(2, 2), dtype=float32) [[1. 2. 3.] [4. 5. 6.]] [[ 1. 4. 9.] [16. 25. 36.]] tf.Tensor( [[1. 2. 3.] [4. 5. 6.]], shape=(2, 3), dtype=float64) tf.Tensor(2.718, shape=(), dtype=float32) 2.718 () tf.Tensor(b'coffee', shape=(), dtype=string) tf.Tensor(6, shape=(), dtype=int32) tf.Tensor(6, shape=(), dtype=int32) tf.Tensor([ 99 111 102 102 101 101], shape=(6,), dtype=int32) tf.Tensor([b'cafe' b'coffee' b'\xe5\x92\x96\xe5\x95\xa1'], shape=(3,), dtype=string) tf.Tensor([4 6 2], shape=(3,), dtype=int32) <tf.RaggedTensor [[99, 97, 102, 101], [99, 111, 102, 102, 101, 101], [21654, 21857]]> <tf.RaggedTensor [[11, 12], [21, 22, 23], [], [41]]> tf.Tensor([21 22 23], shape=(3,), dtype=int32) <tf.RaggedTensor [[21, 22, 23], []]> <tf.RaggedTensor [[11, 12], [21, 22, 23], [], [41], [51, 52], [], [71], [42, 43]]> <tf.RaggedTensor [[11, 12, 51, 52], [21, 22, 23], [71], [41, 42, 43]]> tf.Tensor( [[11 12 0] [21 22 23] [ 0 0 0] [41 0 0]], shape=(4, 3), dtype=int32) SparseTensor(indices=tf.Tensor( [[0 1] [1 0] [2 3]], shape=(3, 2), dtype=int64), values=tf.Tensor([1. 2. 3.], shape=(3,), dtype=float32), dense_shape=tf.Tensor([3 4], shape=(2,), dtype=int64)) tf.Tensor( [[0. 1. 0. 0.] [2. 0. 0. 0.] [0. 0. 0. 3.]], shape=(3, 4), dtype=float32) SparseTensor(indices=tf.Tensor( [[0 1] [1 0] [2 3]], shape=(3, 2), dtype=int64), values=tf.Tensor([2. 4. 6.], shape=(3,), dtype=float32), dense_shape=tf.Tensor([3 4], shape=(2,), dtype=int64)) unsupported operand type(s) for +: 'SparseTensor' and 'float' tf.Tensor( [[ 30. 40.] [ 20. 40.] [210. 240.]], shape=(3, 2), dtype=float32) SparseTensor(indices=tf.Tensor( [[0 2] [0 1] [2 3]], shape=(3, 2), dtype=int64), values=tf.Tensor([1. 2. 3.], shape=(3,), dtype=float32), dense_shape=tf.Tensor([3 4], shape=(2,), dtype=int64)) indices[1] = [0,1] is out of order [Op:SparseToDense] tf.Tensor( [[0. 2. 1. 0.] [0. 0. 0. 0.] [0. 0. 0. 3.]], shape=(3, 4), dtype=float32)

现在我们来看一下它的变量操作

 import tensorflow as tf import numpy as np if __name__ == "__main__": v = tf.Variable([[1., 2., 3.], [4., 5., 6.]]) print(v) # 转化为常量  print(v.value()) print(v.numpy()) # 重新赋值  v.assign(2 * v) print(v) # 给变量的某个位置重新赋值  v[0, 1].assign(42) print(v) # 给变量的某一行重新赋值  v[1].assign([7., 8., 9.]) print(v) # 不能直接使用=赋值  try: v[0] = [10., 20., 30.] except TypeError as ex: print(ex)

运行结果

 <tf.Variable 'Variable:0' shape=(2, 3) dtype=float32, numpy= array([[1., 2., 3.], [4., 5., 6.]], dtype=float32)> tf.Tensor( [[1. 2. 3.] [4. 5. 6.]], shape=(2, 3), dtype=float32) [[1. 2. 3.] [4. 5. 6.]] <tf.Variable 'Variable:0' shape=(2, 3) dtype=float32, numpy= array([[ 2., 4., 6.], [ 8., 10., 12.]], dtype=float32)> <tf.Variable 'Variable:0' shape=(2, 3) dtype=float32, numpy= array([[ 2., 42., 6.], [ 8., 10., 12.]], dtype=float32)> <tf.Variable 'Variable:0' shape=(2, 3) dtype=float32, numpy= array([[ 2., 42., 6.], [ 7., 8., 9.]], dtype=float32)> 'ResourceVariable' object does not support item assignment

自定义损失函数

这里我们还是以加利福尼亚的房价回归问题来说明

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import time import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers from sklearn.datasets import fetch_california_housing import pprint from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler if __name__ == "__main__": housing = fetch_california_housing() # print(housing.DESCR)  # print(housing.data.shape)  # print(housing.target.shape)  # pprint.pprint(housing.data[0:5])  # pprint.pprint(housing.target[0:5])  X_train_all, X_test, y_train_all, y_test = train_test_split(housing.data, housing.target, random_state=7) X_train, X_valid, y_train, y_valid = train_test_split(X_train_all, y_train_all, random_state=11) # print(X_train.shape, y_train.shape)  # print(X_valid.shape, y_valid.shape)  # print(X_test.shape, y_test.shape)  scaler = StandardScaler() # 归一化  X_train = scaler.fit_transform(X_train) X_valid = scaler.transform(X_valid) X_test = scaler.transform(X_test) def customized_mse(y_true, y_pred): # 自定义损失函数  return tf.reduce_mean(tf.square(y_pred - y_true)) model = keras.models.Sequential([ layers.Dense(30, activation='relu', input_shape=X_train.shape[1:]),  layers.Dense(1) ]) print(model.summary()) # 使用均方误差损失函数和随机梯度下降法  model.compile(loss=customized_mse, optimizer=optimizers.SGD(learning_rate=0.01),  metrics=['mean_squared_error']) callbacks = [keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3)] history = model.fit(X_train, y_train, validation_data=(X_valid, y_valid),  epochs=100, callbacks=callbacks) print(model.evaluate(X_test, y_test)) def plot_learning_curves(history): # 学习曲线  pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history)

运行结果

 Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= dense (Dense) (None, 30) 270 _________________________________________________________________ dense_1 (Dense) (None, 1) 31 ================================================================= Total params: 301 Trainable params: 301 Non-trainable params: 0 _________________________________________________________________ None Train on 11610 samples, validate on 3870 samples Epoch 1/100 11610/11610 [==============================] - 1s 119us/sample - loss: 1.5018 - mean_squared_error: 1.5018 - val_loss: 0.8721 - val_mean_squared_error: 0.8721 Epoch 2/100 11610/11610 [==============================] - 0s 43us/sample - loss: 1.8099 - mean_squared_error: 1.8099 - val_loss: 0.5967 - val_mean_squared_error: 0.5967 Epoch 3/100 11610/11610 [==============================] - 1s 43us/sample - loss: 0.4971 - mean_squared_error: 0.4971 - val_loss: 0.4621 - val_mean_squared_error: 0.4621 Epoch 4/100 11610/11610 [==============================] - 0s 43us/sample - loss: 0.4396 - mean_squared_error: 0.4396 - val_loss: 0.4405 - val_mean_squared_error: 0.4405 Epoch 5/100 11610/11610 [==============================] - 0s 43us/sample - loss: 0.4121 - mean_squared_error: 0.4121 - val_loss: 0.4133 - val_mean_squared_error: 0.4133 Epoch 6/100 11610/11610 [==============================] - 0s 43us/sample - loss: 0.4043 - mean_squared_error: 0.4043 - val_loss: 0.4039 - val_mean_squared_error: 0.4039 Epoch 7/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3896 - mean_squared_error: 0.3896 - val_loss: 0.4000 - val_mean_squared_error: 0.4000 Epoch 8/100 11610/11610 [==============================] - 1s 70us/sample - loss: 0.3796 - mean_squared_error: 0.3796 - val_loss: 0.3936 - val_mean_squared_error: 0.3936 Epoch 9/100 11610/11610 [==============================] - 0s 43us/sample - loss: 0.3771 - mean_squared_error: 0.3771 - val_loss: 0.5541 - val_mean_squared_error: 0.5541 Epoch 10/100 11610/11610 [==============================] - 1s 46us/sample - loss: 0.3820 - mean_squared_error: 0.3820 - val_loss: 0.3874 - val_mean_squared_error: 0.3874 Epoch 11/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3686 - mean_squared_error: 0.3686 - val_loss: 0.3758 - val_mean_squared_error: 0.3758 Epoch 12/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3666 - mean_squared_error: 0.3666 - val_loss: 0.3867 - val_mean_squared_error: 0.3867 Epoch 13/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3632 - mean_squared_error: 0.3632 - val_loss: 0.3711 - val_mean_squared_error: 0.3711 Epoch 14/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3592 - mean_squared_error: 0.3592 - val_loss: 0.3790 - val_mean_squared_error: 0.3790 Epoch 15/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3578 - mean_squared_error: 0.3578 - val_loss: 0.3687 - val_mean_squared_error: 0.3687 Epoch 16/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3547 - mean_squared_error: 0.3547 - val_loss: 0.3691 - val_mean_squared_error: 0.3691 Epoch 17/100 11610/11610 [==============================] - 1s 52us/sample - loss: 0.3530 - mean_squared_error: 0.3530 - val_loss: 0.3690 - val_mean_squared_error: 0.3690 Epoch 18/100 11610/11610 [==============================] - 1s 54us/sample - loss: 0.3549 - mean_squared_error: 0.3549 - val_loss: 0.3625 - val_mean_squared_error: 0.3625 Epoch 19/100 11610/11610 [==============================] - 1s 54us/sample - loss: 0.3506 - mean_squared_error: 0.3506 - val_loss: 0.3605 - val_mean_squared_error: 0.3605 Epoch 20/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3481 - mean_squared_error: 0.3481 - val_loss: 0.3610 - val_mean_squared_error: 0.3610 Epoch 21/100 11610/11610 [==============================] - 1s 72us/sample - loss: 0.3479 - mean_squared_error: 0.3479 - val_loss: 0.3601 - val_mean_squared_error: 0.3601 Epoch 22/100 11610/11610 [==============================] - 1s 63us/sample - loss: 0.3448 - mean_squared_error: 0.3448 - val_loss: 0.3578 - val_mean_squared_error: 0.3578 Epoch 23/100 11610/11610 [==============================] - 1s 73us/sample - loss: 0.3457 - mean_squared_error: 0.3457 - val_loss: 0.3611 - val_mean_squared_error: 0.3611 Epoch 24/100 11610/11610 [==============================] - 0s 42us/sample - loss: 0.3447 - mean_squared_error: 0.3447 - val_loss: 0.3539 - val_mean_squared_error: 0.3539 Epoch 25/100 11610/11610 [==============================] - 1s 55us/sample - loss: 0.3432 - mean_squared_error: 0.3432 - val_loss: 0.3515 - val_mean_squared_error: 0.3515 Epoch 26/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3404 - mean_squared_error: 0.3404 - val_loss: 0.3544 - val_mean_squared_error: 0.3544 Epoch 27/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3406 - mean_squared_error: 0.3406 - val_loss: 0.3504 - val_mean_squared_error: 0.3504 Epoch 28/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3389 - mean_squared_error: 0.3389 - val_loss: 0.3514 - val_mean_squared_error: 0.3514 Epoch 29/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3385 - mean_squared_error: 0.3385 - val_loss: 0.3470 - val_mean_squared_error: 0.3470 Epoch 30/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3375 - mean_squared_error: 0.3375 - val_loss: 0.3513 - val_mean_squared_error: 0.3513 Epoch 31/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3362 - mean_squared_error: 0.3362 - val_loss: 0.3474 - val_mean_squared_error: 0.3474 Epoch 32/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3351 - mean_squared_error: 0.3351 - val_loss: 0.3493 - val_mean_squared_error: 0.3493 Epoch 33/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3349 - mean_squared_error: 0.3349 - val_loss: 0.3461 - val_mean_squared_error: 0.3461 Epoch 34/100 11610/11610 [==============================] - 0s 41us/sample - loss: 0.3326 - mean_squared_error: 0.3326 - val_loss: 0.3464 - val_mean_squared_error: 0.3464 5160/1 [=====================================================] - 0s 20us/sample - loss: 0.5104 - mean_squared_error: 0.3525 [0.3524518048116403, 0.3524517]

这里我们可以看到我们自己实现的均方误差损失函数和系统自带的均方误差损失函数是一样，他们损失函数值曲线是重合的。

自定义Layers

我们先来看一下Layers的一些特性

 import tensorflow as tf from tensorflow.keras import layers if __name__ == "__main__": # 我们一般会在全连接层的第一层的时候输入input_shape  # 不使用input_shape也没关系，它会在第一次运行的时候推导出来  layer = layers.Dense(100, input_shape=(None, 5)) # 这里会点乘一个[5, 100]的矩阵转成[None, 100]的输出  print(layer(tf.zeros([10, 5]))) # 打印该层所有的参数  print(layer.variables) # 打印该层所有可训练的参数  print(layer.trainable_variables)

运行结果

 tf.Tensor( [[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 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-0.18907636, 0.03709231, -0.02248657, 0.03133444, -0.1615734 ], [-0.16601531, 0.21792419, -0.1103511 , 0.0025705 , -0.05631484, 0.07372896, 0.18572135, -0.07337801, -0.01120584, -0.13398278, -0.04314138, 0.17321984, 0.11909981, -0.15493754, 0.07232957, 0.13085563, -0.2287109 , -0.21197955, 0.1428767 , 0.1137528 , -0.14559013, 0.13985835, 0.12416814, -0.05637537, -0.0046737 , 0.00876671, 0.05863507, -0.03590567, 0.10624601, -0.1412015 , 0.15561827, 0.10837926, -0.1810194 , -0.05347614, 0.03898682, -0.10682511, -0.16920623, -0.18795235, -0.08359696, 0.18185644, -0.19991723, -0.05360089, 0.13864844, 0.1414309 , -0.23352294, 0.21933769, -0.2087497 , 0.02414815, -0.20864718, -0.01974651, -0.12589416, -0.04501775, 0.09451391, 0.01687138, 0.13819186, -0.21920864, 0.22943564, 0.22025959, 0.07460229, -0.11851113, 0.04449643, -0.11150999, 0.18484862, 0.18422444, -0.19684097, 0.125441 , 0.16443445, 0.174614 , 0.21528427, -0.02458197, 0.2311335 , -0.20051023, 0.16148575, 0.03468569, 0.08386306, 0.18408652, -0.09470819, -0.22607385, -0.04776055, 0.17687435, 0.01153742, 0.15740515, 0.22579281, 0.2256033 , 0.23760812, -0.08624862, -0.04818098, -0.09573658, 0.00707476, -0.174594 , 0.17612858, -0.02651523, -0.03352439, -0.0982894 , 0.12405153, 0.1423658 , 0.12438641, -0.22709328, 0.18641399, -0.0159114 ]], dtype=float32)>, <tf.Variable 'dense/bias:0' shape=(100,) dtype=float32, numpy= array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], dtype=float32)>]

通过结果我们可以看出layer的输出结果是一个常量，而它的参数是两个变量。其中dense/kernel:0就是我们经常说的线性模型Wx+b中的系数W，而dense/bias:0就是其中的截距b。而且在这里它的参数和可训练的参数是一致的。现在我们来实现自定义的Dense_Layer。

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import time import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers from sklearn.datasets import fetch_california_housing import pprint from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler if __name__ == "__main__": housing = fetch_california_housing() # print(housing.DESCR)  # print(housing.data.shape)  # print(housing.target.shape)  # pprint.pprint(housing.data[0:5])  # pprint.pprint(housing.target[0:5])  X_train_all, X_test, y_train_all, y_test = train_test_split(housing.data, housing.target, random_state=7) X_train, X_valid, y_train, y_valid = train_test_split(X_train_all, y_train_all, random_state=11) # print(X_train.shape, y_train.shape)  # print(X_valid.shape, y_valid.shape)  # print(X_test.shape, y_test.shape)  scaler = StandardScaler() # 归一化  X_train = scaler.fit_transform(X_train) X_valid = scaler.transform(X_valid) X_test = scaler.transform(X_test) def customized_mse(y_true, y_pred): # 自定义损失函数  return tf.reduce_mean(tf.square(y_pred - y_true)) class CustomizedDenseLayer(layers.Layer): # 自定义DenseLayer   def __init__(self, units, activation=None, **kwargs): '''  :param units: 输出大小  :param activation: 激活函数  :param kwargs:  '''  self.units = units self.activation = layers.Activation(activation=activation) super(CustomizedDenseLayer, self).__init__(**kwargs) def build(self, input_shape): '''  构建所需要的参数  :param input_shape: 输入的形状  :return:  '''  # Wx + b，input_shape:[None, a],W:[a, b],output_shape:[None, b]  # shape为W的形状，即变换矩阵  # uniform表示均匀分布的方式初始化  # trainable = True表示参数是可以被训练的  self.kernel = self.add_weight(name='kernel',  shape=(input_shape[1], self.units),  initializer='uniform',  trainable=True) self.bias = self.add_weight(name='bias',  shape=(self.units,),  initializer='zeros',  trainable=True) super(CustomizedDenseLayer, self).build(input_shape) def call(self, X): # 完成正向计算  return self.activation(X @ self.kernel + self.bias) model = keras.models.Sequential([ CustomizedDenseLayer(30, activation='relu', input_shape=X_train.shape[1:]),  CustomizedDenseLayer(1) ]) print(model.summary()) # 使用均方误差损失函数和随机梯度下降法  model.compile(loss=customized_mse, optimizer=optimizers.SGD(learning_rate=0.01),  metrics=['mean_squared_error']) callbacks = [keras.callbacks.EarlyStopping(patience=5, min_delta=1e-3)] history = model.fit(X_train, y_train, validation_data=(X_valid, y_valid),  epochs=100, callbacks=callbacks) print(model.evaluate(X_test, y_test)) def plot_learning_curves(history): # 学习曲线  pd.DataFrame(history.history).plot(figsize=(8, 5)) plt.grid(True) plt.gca().set_ylim(0, 1) plt.show() plot_learning_curves(history)

运行结果

 Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= customized_dense_layer (Cust (None, 30) 270 _________________________________________________________________ customized_dense_layer_1 (Cu (None, 1) 31 ================================================================= Total params: 301 Trainable params: 301 Non-trainable params: 0 _________________________________________________________________ None Train on 11610 samples, validate on 3870 samples Epoch 1/100 11610/11610 [==============================] - 1s 98us/sample - loss: 1.1060 - mean_squared_error: 1.1061 - val_loss: 0.6408 - val_mean_squared_error: 0.6408 Epoch 2/100 11610/11610 [==============================] - 1s 55us/sample - loss: 0.5543 - mean_squared_error: 0.5543 - val_loss: 0.5453 - val_mean_squared_error: 0.5453 Epoch 3/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.4889 - mean_squared_error: 0.4889 - val_loss: 0.4974 - val_mean_squared_error: 0.4974 Epoch 4/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.4619 - mean_squared_error: 0.4619 - val_loss: 0.4884 - val_mean_squared_error: 0.4884 Epoch 5/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.4479 - mean_squared_error: 0.4479 - val_loss: 0.4610 - val_mean_squared_error: 0.4610 Epoch 6/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.4337 - mean_squared_error: 0.4337 - val_loss: 0.4442 - val_mean_squared_error: 0.4442 Epoch 7/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.4234 - mean_squared_error: 0.4234 - val_loss: 0.4362 - val_mean_squared_error: 0.4362 Epoch 8/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.4155 - mean_squared_error: 0.4155 - val_loss: 0.4295 - val_mean_squared_error: 0.4295 Epoch 9/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.4164 - mean_squared_error: 0.4164 - val_loss: 0.4230 - val_mean_squared_error: 0.4230 Epoch 10/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.4067 - mean_squared_error: 0.4067 - val_loss: 0.4183 - val_mean_squared_error: 0.4183 Epoch 11/100 11610/11610 [==============================] - 1s 49us/sample - loss: 0.3986 - mean_squared_error: 0.3986 - val_loss: 0.4144 - val_mean_squared_error: 0.4144 Epoch 12/100 11610/11610 [==============================] - 1s 67us/sample - loss: 0.3946 - mean_squared_error: 0.3946 - val_loss: 0.4088 - val_mean_squared_error: 0.4088 Epoch 13/100 11610/11610 [==============================] - 1s 72us/sample - loss: 0.3923 - mean_squared_error: 0.3923 - val_loss: 0.4127 - val_mean_squared_error: 0.4127 Epoch 14/100 11610/11610 [==============================] - 1s 65us/sample - loss: 0.3895 - mean_squared_error: 0.3895 - val_loss: 0.4019 - val_mean_squared_error: 0.4019 Epoch 15/100 11610/11610 [==============================] - 1s 59us/sample - loss: 0.3863 - mean_squared_error: 0.3863 - val_loss: 0.4008 - val_mean_squared_error: 0.4008 Epoch 16/100 11610/11610 [==============================] - 1s 50us/sample - loss: 0.3835 - mean_squared_error: 0.3835 - val_loss: 0.3949 - val_mean_squared_error: 0.3949 Epoch 17/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3819 - mean_squared_error: 0.3819 - val_loss: 0.3942 - val_mean_squared_error: 0.3942 Epoch 18/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3813 - mean_squared_error: 0.3813 - val_loss: 0.3909 - val_mean_squared_error: 0.3909 Epoch 19/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3784 - mean_squared_error: 0.3784 - val_loss: 0.3882 - val_mean_squared_error: 0.3882 Epoch 20/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3763 - mean_squared_error: 0.3763 - val_loss: 0.3960 - val_mean_squared_error: 0.3960 Epoch 21/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3760 - mean_squared_error: 0.3760 - val_loss: 0.3876 - val_mean_squared_error: 0.3876 Epoch 22/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3730 - mean_squared_error: 0.3730 - val_loss: 0.3885 - val_mean_squared_error: 0.3885 Epoch 23/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3739 - mean_squared_error: 0.3739 - val_loss: 0.3854 - val_mean_squared_error: 0.3854 Epoch 24/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3701 - mean_squared_error: 0.3701 - val_loss: 0.3812 - val_mean_squared_error: 0.3812 Epoch 25/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3697 - mean_squared_error: 0.3697 - val_loss: 0.3796 - val_mean_squared_error: 0.3796 Epoch 26/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3701 - mean_squared_error: 0.3701 - val_loss: 0.3787 - val_mean_squared_error: 0.3787 Epoch 27/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3670 - mean_squared_error: 0.3670 - val_loss: 0.3777 - val_mean_squared_error: 0.3777 Epoch 28/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3661 - mean_squared_error: 0.3661 - val_loss: 0.3761 - val_mean_squared_error: 0.3761 Epoch 29/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3638 - mean_squared_error: 0.3638 - val_loss: 0.3738 - val_mean_squared_error: 0.3738 Epoch 30/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3677 - mean_squared_error: 0.3677 - val_loss: 0.3726 - val_mean_squared_error: 0.3726 Epoch 31/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3637 - mean_squared_error: 0.3637 - val_loss: 0.3703 - val_mean_squared_error: 0.3703 Epoch 32/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3651 - mean_squared_error: 0.3651 - val_loss: 0.3750 - val_mean_squared_error: 0.3750 Epoch 33/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3627 - mean_squared_error: 0.3627 - val_loss: 0.3714 - val_mean_squared_error: 0.3714 Epoch 34/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3593 - mean_squared_error: 0.3593 - val_loss: 0.3701 - val_mean_squared_error: 0.3701 Epoch 35/100 11610/11610 [==============================] - 1s 48us/sample - loss: 0.3582 - mean_squared_error: 0.3582 - val_loss: 0.3681 - val_mean_squared_error: 0.3681 Epoch 36/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3622 - mean_squared_error: 0.3622 - val_loss: 0.3668 - val_mean_squared_error: 0.3668 Epoch 37/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3556 - mean_squared_error: 0.3556 - val_loss: 0.3789 - val_mean_squared_error: 0.3789 Epoch 38/100 11610/11610 [==============================] - 1s 47us/sample - loss: 0.3618 - mean_squared_error: 0.3618 - val_loss: 0.3651 - val_mean_squared_error: 0.3651 Epoch 39/100 11610/11610 [==============================] - 1s 64us/sample - loss: 0.3546 - mean_squared_error: 0.3546 - val_loss: 0.3630 - val_mean_squared_error: 0.3630 Epoch 40/100 11610/11610 [==============================] - 1s 69us/sample - loss: 0.3533 - mean_squared_error: 0.3533 - val_loss: 0.3897 - val_mean_squared_error: 0.3897 Epoch 41/100 11610/11610 [==============================] - 1s 65us/sample - loss: 0.3589 - mean_squared_error: 0.3589 - val_loss: 0.3621 - val_mean_squared_error: 0.3621 Epoch 42/100 11610/11610 [==============================] - 1s 84us/sample - loss: 0.3540 - mean_squared_error: 0.3540 - val_loss: 0.3648 - val_mean_squared_error: 0.3648 Epoch 43/100 11610/11610 [==============================] - 1s 62us/sample - loss: 0.3554 - mean_squared_error: 0.3554 - val_loss: 0.3638 - val_mean_squared_error: 0.3638 Epoch 44/100 11610/11610 [==============================] - 1s 61us/sample - loss: 0.3512 - mean_squared_error: 0.3512 - val_loss: 0.3575 - val_mean_squared_error: 0.3575 Epoch 45/100 11610/11610 [==============================] - 1s 65us/sample - loss: 0.3549 - mean_squared_error: 0.3549 - val_loss: 0.3566 - val_mean_squared_error: 0.3566 Epoch 46/100 11610/11610 [==============================] - 1s 79us/sample - loss: 0.3497 - mean_squared_error: 0.3497 - val_loss: 0.3561 - val_mean_squared_error: 0.3561 Epoch 47/100 11610/11610 [==============================] - 1s 86us/sample - loss: 0.3470 - mean_squared_error: 0.3470 - val_loss: 0.3584 - val_mean_squared_error: 0.3584 Epoch 48/100 11610/11610 [==============================] - 1s 74us/sample - loss: 0.3470 - mean_squared_error: 0.3470 - val_loss: 0.3526 - val_mean_squared_error: 0.3526 Epoch 49/100 11610/11610 [==============================] - 1s 51us/sample - loss: 0.3469 - mean_squared_error: 0.3469 - val_loss: 0.3529 - val_mean_squared_error: 0.3529 Epoch 50/100 11610/11610 [==============================] - 1s 60us/sample - loss: 0.3492 - mean_squared_error: 0.3492 - val_loss: 0.3531 - val_mean_squared_error: 0.3531 Epoch 51/100 11610/11610 [==============================] - 1s 70us/sample - loss: 0.3428 - mean_squared_error: 0.3428 - val_loss: 0.3601 - val_mean_squared_error: 0.3601 Epoch 52/100 11610/11610 [==============================] - 1s 73us/sample - loss: 0.3448 - mean_squared_error: 0.3448 - val_loss: 0.3517 - val_mean_squared_error: 0.3517 Epoch 53/100 11610/11610 [==============================] - 1s 64us/sample - loss: 0.3423 - mean_squared_error: 0.3423 - val_loss: 0.3618 - val_mean_squared_error: 0.3618 5160/1 [===================================================] - 0s 23us/sample - loss: 0.4712 - mean_squared_error: 0.3614 [0.36136142297308577, 0.3613615]

在这里，我们可以看到使用子类的方式来定义层次是比较繁琐和复杂的，如果我们只是想增加一个激活函数层，这样写就显得比较累赘了，所以我们可以使用lambda表达式来完成这个功能

 import tensorflow as tf from tensorflow.keras import layers, models import numpy as np if __name__ == "__main__": # 添加激活函数层sotgplus:log(1+e^x)  customized_softplus = layers.Lambda(lambda x: tf.nn.softplus(x)) print(customized_softplus([-10., -5., 0., 5., 10.])) model = models.Sequential([ layers.Dense(30, activation='relu', input_shape=[None, 5]),  layers.Dense(1),  customized_softplus # 它等同于下面任意一行代码  # layers.Dense(1, activation='softplus'),  # layers.Dense(1), layers.Activation('softplus')  ]) print(model.summary())

运行结果

 tf.Tensor([4.5417706e-05 6.7153489e-03 6.9314718e-01 5.0067153e+00 1.0000046e+01], shape=(5,), dtype=float32) Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= dense (Dense) (None, None, 30) 180 _________________________________________________________________ dense_1 (Dense) (None, None, 1) 31 _________________________________________________________________ lambda (Lambda) (None, None, 1) 0 ================================================================= Total params: 211 Trainable params: 211 Non-trainable params: 0 _________________________________________________________________ None

tf.function函数转换图结构

这里我们有一个概念，那就是tensorflow的类型(常量，变量)以及它的函数都是被优化过，更加适合于使用GPU、TPU进行加速，那么对于普通的Python库函数是没有这个功能的。那么对于普通的Python库函数能否使用tensorflow的这种优化呢，答案是肯定的。

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import timeit import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers if __name__ == "__main__": def scaled_elu(z, scale=1.0, alpha=1.0): # z >= 0 ? scale * z : scale * alpha * tf.nn.elu(z) is_positive = tf.greater_equal(z, 0.0) return scale * tf.where(is_positive, z, alpha * tf.nn.elu(z)) t1 = tf.constant(-3.) t2 = tf.constant([-3., -2.5]) print(scaled_elu(t1)) print(scaled_elu(t2)) scaled_elu_tf = tf.function(scaled_elu) print(scaled_elu_tf(t1)) print(scaled_elu_tf(t2)) print(scaled_elu_tf.python_function is scaled_elu) %timeit scaled_elu(tf.random.normal((1000, 1000))) %timeit scaled_elu_tf(tf.random.normal((1000, 1000)))

运行结果

 tf.Tensor(-0.95021296, shape=(), dtype=float32) tf.Tensor([-0.95021296 -0.917915 ], shape=(2,), dtype=float32) tf.Tensor(-0.95021296, shape=(), dtype=float32) tf.Tensor([-0.95021296 -0.917915 ], shape=(2,), dtype=float32) True 10 loops, best of 5: 25.8 ms per loop 10 loops, best of 5: 23.7 ms per loop

这里我们可以把scaled_elu看成是一个普通的Python函数，当我们对这个函数进行了图模型化scaled_elu_tf = tf.function(scaled_elu)后，当我们对其进行大型矩阵计算中，我们可以看到图模型化后的scaled_elu_tf比之前scaled_elu快了一点点。不过这里必须使用TPU环境才有效果，否则是比较慢的。除了这种直接转的方式，我们还可以通过打标签的方式

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import timeit import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers if __name__ == "__main__": def scaled_elu(z, scale=1.0, alpha=1.0): # z >= 0 ? scale * z : scale * alpha * tf.nn.elu(z) is_positive = tf.greater_equal(z, 0.0) return scale * tf.where(is_positive, z, alpha * tf.nn.elu(z)) t1 = tf.constant(-3.) t2 = tf.constant([-3., -2.5]) print(scaled_elu(t1)) print(scaled_elu(t2)) scaled_elu_tf = tf.function(scaled_elu) print(scaled_elu_tf(t1)) print(scaled_elu_tf(t2)) print(scaled_elu_tf.python_function is scaled_elu) %timeit scaled_elu(tf.random.normal((1000, 1000))) %timeit scaled_elu_tf(tf.random.normal((1000, 1000))) @tf.function def converge_to_2(n_iters): # 1 + 1/2 + 1/2^2 + ... + 1/2^n total = tf.constant(0.) increment = tf.constant(1.) for _ in range(n_iters): total += increment increment /= 2.0 return total print(converge_to_2(20))

运行结果

 tf.Tensor(-0.95021296, shape=(), dtype=float32) tf.Tensor([-0.95021296 -0.917915 ], shape=(2,), dtype=float32) tf.Tensor(-0.95021296, shape=(), dtype=float32) tf.Tensor([-0.95021296 -0.917915 ], shape=(2,), dtype=float32) True 10 loops, best of 5: 26 ms per loop 10 loops, best of 5: 24 ms per loop tf.Tensor(1.9999981, shape=(), dtype=float32)

我们可以来看一下这两个函数转成图结构后的代码

 import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import sklearn import pandas as pd import os import sys import timeit import tensorflow as tf from tensorflow import keras from tensorflow.keras import layers, optimizers from IPython.display import display, Markdown if __name__ == "__main__": def scaled_elu(z, scale=1.0, alpha=1.0): # z >= 0 ? scale * z : scale * alpha * tf.nn.elu(z) is_positive = tf.greater_equal(z, 0.0) return scale * tf.where(is_positive, z, alpha * tf.nn.elu(z)) t1 = tf.constant(-3.) t2 = tf.constant([-3., -2.5]) print(scaled_elu(t1)) print(scaled_elu(t2)) scaled_elu_tf = tf.function(scaled_elu) print(scaled_elu_tf(t1)) print(scaled_elu_tf(t2)) print(scaled_elu_tf.python_function is scaled_elu) %timeit scaled_elu(tf.random.normal((1000, 1000))) %timeit scaled_elu_tf(tf.random.normal((1000, 1000))) # @tf.function def converge_to_2(n_iters): # 1 + 1/2 + 1/2^2 + ... + 1/2^n total = tf.constant(0.) increment = tf.constant(1.) for _ in range(n_iters): total += increment increment /= 2.0 return total print(converge_to_2(20)) def display_tf_code(func): code = tf.autograph.to_code(func) display(Markdown('```python\n{}\n```'.format(code))) display_tf_code(scaled_elu) display_tf_code(converge_to_2)

运行结果

 tf.Tensor(-0.95021296, shape=(), dtype=float32) tf.Tensor([-0.95021296 -0.917915 ], shape=(2,), dtype=float32) tf.Tensor(-0.95021296, shape=(), dtype=float32) tf.Tensor([-0.95021296 -0.917915 ], shape=(2,), dtype=float32) True 10 loops, best of 5: 25.7 ms per loop 10 loops, best of 5: 23.9 ms per loop tf.Tensor(1.9999981, shape=(), dtype=float32) def tf__scaled_elu(z, scale=None, alpha=None): with ag__.FunctionScope('scaled_elu', 'fscope', ag__.ConversionOptions(recursive=True, user_requested=True, optional_features=(), internal_convert_user_code=True)) as fscope: do_return = False retval_ = ag__.UndefinedReturnValue() is_positive = ag__.converted_call(ag__.ld(tf).greater_equal, (ag__.ld(z), 0.0), None, fscope) try: do_return = True retval_ = (ag__.ld(scale) * ag__.converted_call(ag__.ld(tf).where, (ag__.ld(is_positive), ag__.ld(z), (ag__.ld(alpha) * ag__.converted_call(ag__.ld(tf).nn.elu, (ag__.ld(z),), None, fscope))), None, fscope)) except: do_return = False raise return fscope.ret(retval_, do_return) def tf__converge_to(n_iters): with ag__.FunctionScope('converge_to_2', 'fscope', ag__.ConversionOptions(recursive=True, user_requested=True, optional_features=(), internal_convert_user_code=True)) as fscope: do_return = False retval_ = ag__.UndefinedReturnValue() total = ag__.converted_call(ag__.ld(tf).constant, (0.0,), None, fscope) increment = ag__.converted_call(ag__.ld(tf).constant, (1.0,), None, fscope) def get_state(): return (total, increment) def set_state(vars_): nonlocal increment, total (total, increment) = vars_ def loop_body(itr): nonlocal increment, total _ = itr total = ag__.ld(total) total += increment increment = ag__.ld(increment) increment /= 2.0 _ = ag__.Undefined('_') ag__.for_stmt(ag__.converted_call(ag__.ld(range), (ag__.ld(n_iters),), None, fscope), None, loop_body, get_state, set_state, ('total', 'increment'), {'iterate_names': '_'}) try: do_return = True retval_ = ag__.ld(total) except: do_return = False raise return fscope.ret(retval_, do_return)

之前我们使用的都是常量，现在我们来看看对于变量来说，是什么情况

 def add_21(): var = tf.Variable(0.) return var.assign_add(21) # += print(add_21())

运行结果

 <tf.Variable 'UnreadVariable' shape=() dtype=float32, numpy=21.0>

现在我们给这段代码加上标签

 @tf.function def add_21(): var = tf.Variable(0.) return var.assign_add(21) # += print(add_21())

运行结果

 --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-8-806807c51c7b> in <module>() 4 return var.assign_add(21) # += 5 ----> 6 print(add_21()) 7 frames /usr/local/lib/python3.7/dist-packages/tensorflow/python/framework/func_graph.py in wrapper(*args, **kwargs) 992 except Exception as e: # pylint:disable=broad-except 993 if hasattr(e, "ag_error_metadata"): --> 994 raise e.ag_error_metadata.to_exception(e) 995 else: 996 raise ValueError: in user code: <ipython-input-8-806807c51c7b>:3 add_21 * var = tf.Variable(0.) /usr/local/lib/python3.7/dist-packages/tensorflow/python/ops/variables.py:268 __call__ ** return cls._variable_v2_call(*args, **kwargs) /usr/local/lib/python3.7/dist-packages/tensorflow/python/ops/variables.py:262 _variable_v2_call shape=shape) /usr/local/lib/python3.7/dist-packages/tensorflow/python/ops/variables.py:67 getter return captured_getter(captured_previous, **kwargs) /usr/local/lib/python3.7/dist-packages/tensorflow/python/eager/def_function.py:765 invalid_creator_scope "tf.function-decorated function tried to create " ValueError: tf.function-decorated function tried to create variables on non-first call.

它会直接报错，这个主要是对于tensorflow的图结构来说，它是不能直接在函数内部定义变量的，所以我们需要将变量定义到函数外部。

 var = tf.Variable(0.) @tf.function def add_21(): return var.assign_add(21) # += print(add_21())

运行结果

 tf.Tensor(21.0, shape=(), dtype=float32)

由于Python是一个弱类型的语言，有的时候它可以输入多种不同的类型，现在我们要给图结构函数限制输入的类型

 @tf.function(input_signature=[tf.TensorSpec([None], tf.int32, name='x')]) def cube(z): return tf.pow(z, 3) print(cube(tf.constant([1., 2., 3.]))) print(cube(tf.constant([1, 2, 3])))

运行结果

 --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-10-53f91d549b69> in <module>() 3 return tf.pow(z, 3) 4 ----> 5 print(cube(tf.constant([1., 2., 3.]))) 6 print(cube(tf.constant([1, 2, 3]))) 3 frames /usr/local/lib/python3.7/dist-packages/tensorflow/python/eager/function.py in _convert_inputs_to_signature(inputs, input_signature, flat_input_signature) 2890 flatten_inputs)): 2891 raise ValueError("Python inputs incompatible with input_signature:\n%s" % -> 2892 format_error_message(inputs, input_signature)) 2893 2894 if need_packing: ValueError: Python inputs incompatible with input_signature: inputs: ( tf.Tensor([1. 2. 3.], shape=(3,), dtype=float32)) input_signature: ( TensorSpec(shape=(None,), dtype=tf.int32, name='x'))

这里我们给输入的参数限定为int32的整型，当我们输入整型的时候

 @tf.function(input_signature=[tf.TensorSpec([None], tf.int32, name='x')]) def cube(z): return tf.pow(z, 3) # print(cube(tf.constant([1., 2., 3.]))) print(cube(tf.constant([1, 2, 3])))

运行结果

 tf.Tensor([ 1 8 27], shape=(3,), dtype=int32)

现在我们来看一下这个图的一些信息

 # get_concrete_function -> 添加输入签名 ->保存模型 cube_func_int32 = cube.get_concrete_function(tf.TensorSpec([None], tf.int32)) print(cube_func_int32) print(cube_func_int32 is cube.get_concrete_function(tf.TensorSpec([5], tf.int32))) print(cube_func_int32 is cube.get_concrete_function(tf.constant([1, 2, 3])))

运行结果

 ConcreteFunction cube(z) Args: z: int32 Tensor, shape=(None,) Returns: int32 Tensor, shape=(None,) True True

在cube_func_int32对象中就有图的信息

 print(cube_func_int32.graph) # 查看图中的操作 print(cube_func_int32.graph.get_operations()) # 查看立方操作 pow_op = cube_func_int32.graph.get_operations()[2] print(pow_op) # 查看该操作的输入和输出 print(list(pow_op.inputs)) print(list(pow_op.outputs)) # 通过操作名字获取操作 print(cube_func_int32.graph.get_operation_by_name("x")) # 通过张量名字获取操作 print(cube_func_int32.graph.get_tensor_by_name("x:0")) # 打印图定义 print(cube_func_int32.graph.as_graph_def())

运行结果

 FuncGraph(name=cube, id=140354824183312) [<tf.Operation 'x' type=Placeholder>, <tf.Operation 'Pow/y' type=Const>, <tf.Operation 'Pow' type=Pow>, <tf.Operation 'Identity' type=Identity>] name: "Pow" op: "Pow" input: "x" input: "Pow/y" attr { key: "T" value { type: DT_INT32 } } [<tf.Tensor 'x:0' shape=(None,) dtype=int32>, <tf.Tensor 'Pow/y:0' shape=() dtype=int32>] [<tf.Tensor 'Pow:0' shape=(None,) dtype=int32>] name: "x" op: "Placeholder" attr { key: "_user_specified_name" value { s: "x" } } attr { key: "dtype" value { type: DT_INT32 } } attr { key: "shape" value { shape { dim { size: -1 } } } } Tensor("x:0", shape=(None,), dtype=int32) node { name: "x" op: "Placeholder" attr { key: "_user_specified_name" value { s: "x" } } attr { key: "dtype" value { type: DT_INT32 } } attr { key: "shape" value { shape { dim { size: -1 } } } } } node { name: "Pow/y" op: "Const" attr { key: "dtype" value { type: DT_INT32 } } attr { key: "value" value { tensor { dtype: DT_INT32 tensor_shape { } int_val: 3 } } } } node { name: "Pow" op: "Pow" input: "x" input: "Pow/y" attr { key: "T" value { type: DT_INT32 } } } node { name: "Identity" op: "Identity" input: "Pow" attr { key: "T" value { type: DT_INT32 } } } versions { producer: 808 } 

我们这里可以看到该图中有4个操作，这里有Placeholder的概念，Placeholder是tensorflow1中经常用到的图，可以显示定义，在2.0中就不需要了，它是用来放输入的，必须要放进去一个输入才能得到一个输出。那么图信息对我们有什么用呢？一般会用在两个地方，第一个地方就是如何去保存模型；第二个地方就是一旦保存了模型之后，如何把一个模型给载入进来，然后我们载入模型去做infos的时候会经常用到上面这些函数。