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高基数类别特征预处理:平均数编码

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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

在回归场景下表示 类别特征为 k 时对应目标变量的均值。

3. λ 为权重函数,本文中的权重函数公式相较于原论文做了变换,是一个单调递减函数,函数公式:

其中 输入是特征类别在训练集中出现的次数 n,权重函数有两个参数:

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

一个 yi​的概率值必然和其他 yi​的概率值线性相关,因此为了避免多重共线性问题,采用平均数编码后数据集将增加 C-1 列特征。对于回归问题,采用平均数编码后数据集将增加 1 列特征。

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 pdfrom category_encoders import TargetEncoderdf = 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_encode0	a	1	0.2798011	b	0	0.6218432	a	0	0.2798013	b	1	0.6218434	a	0	0.2798015	a	0	0.2798016	b	1	0.6218437	c	1	0.5000008	c	0	0.5000009	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 TargetEncoderfrom category_encoders.datasets import load_compassX, 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"] = yprint(X)# 结果如下,compass_encode列为结果列:	index	compass	HIER_compass_1	compass_encode	label0	1	N	N	0.622636	11	2	N	N	0.622636	02	3	NE	N	0.903830	13	4	NE	N	0.903830	14	5	NE	N	0.903830	15	6	SE	S	0.176600	06	7	SE	S	0.176600	07	8	S	S	0.460520	18	9	S	S	0.460520	09	10	S	S	0.460520	110	11	S	S	0.460520	011	12	W	W	0.403328	112	13	W	W	0.403328	013	14	W	W	0.403328	014	15	W	W	0.403328	015	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 fk 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 productfrom category_encoders  import TargetEncoderfrom sklearn.model_selection import StratifiedKFold, KFoldclass 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

标签: #c语言编程求平均数 #c语言算平均数代码 #c语言平均值函数