一 前言

对于一个类别特征，如果这个特征的取值非常多，则称它为高基数（high-cardinality）类别特征。在深度学习场景中，对于类别特征我们一般采用Embedding的方式，通过预训练或直接训练的方式将类别特征值编码成向量。在经典机器学习场景中，对于有序类别特征，我们可以使用LabelEncoder进行编码处理，对于低基数无序类别特征（在lightgbm中，默认取值个数小于等于4的类别特征），可以采用OneHotEncoder的方式进行编码，但是对于高基数无序类别特征，若直接采用OneHotEncoder的方式编码，在目前效果比较好的GBDT、Xgboost、lightgbm等树模型中，会出现特征稀疏性的问题，造成维度灾难， 若先对类别取值进行聚类分组，然后再进行OneHot编码，虽然可以降低特征的维度，但是聚类分组过程需要借助较强的业务经验知识。本文介绍一种针对高基数无序类别特征非常有效的预处理方法：平均数编码（Mean Encoding）。在很多数据挖掘类竞赛中，有许多人使用这种方法取得了非常优异的成绩。

二 原理

平均数编码，有些地方也称之为目标编码（Target Encoding），是一种基于目标变量统计（Target Statistics）的有监督编码方式。该方法基于贝叶斯思想，用先验概率和后验概率的加权平均值作为类别特征值的编码值，适用于分类和回归场景。平均数编码的公式如下所示：

其中：

1. prior为先验概率，在分类场景中表示样本属于某一个yi的概率

​其中nyi​​表示y =yi​时的样本数量，ny​表示y的总数量；在回归场景下，先验概率为目标变量均值：

2. posterior为后验概率，在分类场景中表示类别特征为k时样本属于某一个yi​的概率

① k：最小阈值，当n = k时，λ= 0.5，先验概率和后验概率的权重相同；当n < k时，λ> 0.5, 先验概率所占的权重更大。

② f：平滑因子，控制权重函数在拐点处的斜率，f越大，曲线坡度越缓。下面是k=1时，不同f对于权重函数的影响：



由图可知，f越大，权重函数S型曲线越缓，正则效应越强。

对于分类问题，在计算后验概率时，目标变量有C个类别，就有C个后验概率，且满足

三 实践

平均数编码不仅可以对单个类别特征编码，也可以对具有层次结构的类别特征进行编码。比如地区特征，国家包含了省，省包含了市，市包含了街区，对于街区特征，每个街区特征对应的样本数量很少，以至于每个街区特征的编码值接近于先验概率。平均数编码通过加入不同层次的先验概率信息解决该问题。下面将以分类问题对这两个场景进行展开：

1. 单个类别特征编码：



在具体实践时可以借助category_encoders包，代码如下：

 import pandas as pd from category_encoders import TargetEncoder df = pd.DataFrame({'cat': ['a', 'b', 'a', 'b', 'a', 'a', 'b', 'c', 'c', 'd'], 'target': [1, 0, 0, 1, 0, 0, 1, 1, 0, 1]}) te = TargetEncoder(cols=["cat"], min_samples_leaf=2, smoothing=1) df["cat_encode"] = te.transform(df)["cat"] print(df) # 结果如下： cat target cat_encode 0 a 1 0.279801 1 b 0 0.621843 2 a 0 0.279801 3 b 1 0.621843 4 a 0 0.279801 5 a 0 0.279801 6 b 1 0.621843 7 c 1 0.500000 8 c 0 0.500000 9 d 1 0.634471

2. 层次结构类别特征编码：

对以下数据集，方位类别特征具有{'N': ('N', 'NE'), 'S': ('S', 'SE'), 'W': 'W'}层级关系，以compass中类别NE为例计算yi​=1，k = 2 f = 2时编码值，计算公式如下：

其中p1为HIER_compass_1中类别N的编码值，计算可以参考单个类别特征编码: 0.74527，posterior=3/3=1，λ= 0.37754 ，则类别NE的编码值：0.37754 * 0.74527 + （1 - 0.37754）* 1 = 0.90383。



代码如下：

 from category_encoders import TargetEncoder from category_encoders.datasets import load_compass X, y = load_compass() # 层次参数hierarchy可以为字典或者dataframe # 字典形式 hierarchical_map = {'compass': {'N': ('N', 'NE'), 'S': ('S', 'SE'), 'W': 'W'}} te = TargetEncoder(verbose=2, hierarchy=hierarchical_map, cols=['compass'], smoothing=2, min_samples_leaf=2) # dataframe形式，HIER_cols的层级顺序由顶向下 HIER_cols = ['HIER_compass_1'] te = TargetEncoder(verbose=2, hierarchy=X[HIER_cols], cols=['compass'], smoothing=2, min_samples_leaf=2) te.fit(X.loc[:,['compass']], y) X["compass_encode"] = te.transform(X.loc[:,['compass']]) X["label"] = y print(X) # 结果如下，compass_encode列为结果列： index compass HIER_compass_1 compass_encode label 0 1 N N 0.622636 1 1 2 N N 0.622636 0 2 3 NE N 0.903830 1 3 4 NE N 0.903830 1 4 5 NE N 0.903830 1 5 6 SE S 0.176600 0 6 7 SE S 0.176600 0 7 8 S S 0.460520 1 8 9 S S 0.460520 0 9 10 S S 0.460520 1 10 11 S S 0.460520 0 11 12 W W 0.403328 1 12 13 W W 0.403328 0 13 14 W W 0.403328 0 14 15 W W 0.403328 0 15 16 W W 0.403328 1

注意事项：

采用平均数编码，容易引起过拟合，可以采用以下方法防止过拟合：

• 增大正则项f
• k折交叉验证

以下为自行实现的基于k折交叉验证版本的平均数编码，可以应用于二分类、多分类、回归场景中对单一类别特征或具有层次结构类别特征进行编码，该版本中用prior对unknown类别和缺失值编码。

 from itertools import product from category_encoders import TargetEncoder from sklearn.model_selection import StratifiedKFold, KFold class MeanEncoder: def __init__(self, categorical_features, n_splits=5, target_type='classification', min_samples_leaf=2, smoothing=1, hierarchy=None, verbose=0, shuffle=False, random_state=None): """ Parameters ---------- categorical_features: list of str the name of the categorical columns to encode. n_splits: int the number of splits used in mean encoding. target_type: str, 'regression' or 'classification'. min_samples_leaf: int For regularization the weighted average between category mean and global mean is taken. The weight is an S-shaped curve between 0 and 1 with the number of samples for a category on the x-axis. The curve reaches 0.5 at min_samples_leaf. (parameter k in the original paper) smoothing: float smoothing effect to balance categorical average vs prior. Higher value means stronger regularization. The value must be strictly bigger than 0. Higher values mean a flatter S-curve (see min_samples_leaf). hierarchy: dict or dataframe A dictionary or a dataframe to define the hierarchy for mapping. If a dictionary, this contains a dict of columns to map into hierarchies. Dictionary key(s) should be the column name from X which requires mapping. For multiple hierarchical maps, this should be a dictionary of dictionaries. If dataframe: a dataframe defining columns to be used for the hierarchies. Column names must take the form: HIER_colA_1, ... HIER_colA_N, HIER_colB_1, ... HIER_colB_M, ... where [colA, colB, ...] are given columns in cols list. 1:N and 1:M define the hierarchy for each column where 1 is the highest hierarchy (top of the tree). A single column or multiple can be used, as relevant. verbose: int integer indicating verbosity of the output. 0 for none. shuffle : bool, default=False random_state : int or RandomState instance, default=None When `shuffle` is True, `random_state` affects the ordering of the indices, which controls the randomness of each fold for each class. Otherwise, leave `random_state` as `None`. Pass an int for reproducible output across multiple function calls. """ self.categorical_features = categorical_features self.n_splits = n_splits self.learned_stats = {} self.min_samples_leaf = min_samples_leaf self.smoothing = smoothing self.hierarchy = hierarchy self.verbose = verbose self.shuffle = shuffle self.random_state = random_state if target_type == 'classification': self.target_type = target_type self.target_values = [] else: self.target_type = 'regression' self.target_values = None def mean_encode_subroutine(self, X_train, y_train, X_test, variable, target): X_train = X_train[[variable]].copy() X_test = X_test[[variable]].copy() if target is not None: nf_name = '{}_pred_{}'.format(variable, target) X_train['pred_temp'] = (y_train == target).astype(int) # classification else: nf_name = '{}_pred'.format(variable) X_train['pred_temp'] = y_train # regression prior = X_train['pred_temp'].mean() te = TargetEncoder(verbose=self.verbose, hierarchy=self.hierarchy, cols=[variable], smoothing=self.smoothing, min_samples_leaf=self.min_samples_leaf) te.fit(X_train[[variable]], X_train['pred_temp']) tmp_l = te.ordinal_encoder.mapping[0]["mapping"].reset_index() tmp_l.rename(columns={"index":variable, 0:"encode"}, inplace=True) tmp_l.dropna(inplace=True) tmp_r = te.mapping[variable].reset_index() if self.hierarchy is None: tmp_r.rename(columns={variable: "encode", 0:nf_name}, inplace=True) else: tmp_r.rename(columns={"index": "encode", 0:nf_name}, inplace=True) col_avg_y = pd.merge(tmp_l, tmp_r, how="left",on=["encode"]) col_avg_y.drop(columns=["encode"], inplace=True) col_avg_y.set_index(variable, inplace=True) nf_train = X_train.join(col_avg_y, on=variable)[nf_name].values nf_test = X_test.join(col_avg_y, on=variable).fillna(prior, inplace=False)[nf_name].values return nf_train, nf_test, prior, col_avg_y def fit(self, X, y): """ :param X: pandas DataFrame, n_samples * n_features :param y: pandas Series or numpy array, n_samples :return X_new: the transformed pandas DataFrame containing mean-encoded categorical features """ X_new = X.copy() if self.target_type == 'classification': skf = StratifiedKFold(self.n_splits, shuffle=self.shuffle, random_state=self.random_state) else: skf = KFold(self.n_splits, shuffle=self.shuffle, random_state=self.random_state) if self.target_type == 'classification': self.target_values = sorted(set(y)) self.learned_stats = {'{}_pred_{}'.format(variable, target): [] for variable, target in product(self.categorical_features, self.target_values)} for variable, target in product(self.categorical_features, self.target_values): nf_name = '{}_pred_{}'.format(variable, target) X_new.loc[:, nf_name] = np.nan for large_ind, small_ind in skf.split(y, y): nf_large, nf_small, prior, col_avg_y = self.mean_encode_subroutine( X_new.iloc[large_ind], y.iloc[large_ind], X_new.iloc[small_ind], variable, target) X_new.iloc[small_ind, -1] = nf_small self.learned_stats[nf_name].append((prior, col_avg_y)) else: self.learned_stats = {'{}_pred'.format(variable): [] for variable in self.categorical_features} for variable in self.categorical_features: nf_name = '{}_pred'.format(variable) X_new.loc[:, nf_name] = np.nan for large_ind, small_ind in skf.split(y, y): nf_large, nf_small, prior, col_avg_y = self.mean_encode_subroutine( X_new.iloc[large_ind], y.iloc[large_ind], X_new.iloc[small_ind], variable, None) X_new.iloc[small_ind, -1] = nf_small self.learned_stats[nf_name].append((prior, col_avg_y)) return X_new def transform(self, X): """ :param X: pandas DataFrame, n_samples * n_features :return X_new: the transformed pandas DataFrame containing mean-encoded categorical features """ X_new = X.copy() if self.target_type == 'classification': for variable, target in product(self.categorical_features, self.target_values): nf_name = '{}_pred_{}'.format(variable, target) X_new[nf_name] = 0 for prior, col_avg_y in self.learned_stats[nf_name]: X_new[nf_name] += X_new[[variable]].join(col_avg_y, on=variable).fillna(prior, inplace=False)[ nf_name] X_new[nf_name] /= self.n_splits else: for variable in self.categorical_features: nf_name = '{}_pred'.format(variable) X_new[nf_name] = 0 for prior, col_avg_y in self.learned_stats[nf_name]: X_new[nf_name] += X_new[[variable]].join(col_avg_y, on=variable).fillna(prior, inplace=False)[ nf_name] X_new[nf_name] /= self.n_splits return X_new

四 总结

本文介绍了一种对高基数类别特征非常有效的编码方式：平均数编码。详细的讲述了该种编码方式的原理，在实际工程应用中有效避免过拟合的方法，并且提供了一个直接上手的代码版本。

作者：京东保险 赵风龙

来源：京东云开发者社区 转载请注明来源