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模型系列：增益模型Uplift Modeling原理和案例

。这就是为什么我们只能估计 ：

$ \widehat{CATE} (uplift) = E[Y_i|X_i = x, W_i = 1] - E[Y_i|X_i = x, W_i = 0] $，其中 $ Y^1_i = Y_i = Y^1_i if W_i = 1$ and Y i 0 Y^0_i Yi0​ where $W_i = 0 $

注意！ W i W_i Wi​ 应该在给定 X i X_i Xi​ 的条件下与 Y i 1 Y^1_i Yi1​ 和 Y i 0 Y^0_i Yi0​ 独立。

有两种类型的增益模型：

  1. 元学习器 - 转换问题并使用经典的机器学习模型

  2. 直接增益模型 - 直接预测增益的算法。

1. 初步步骤

返回目录


import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from tqdm.notebook import tqdm
import seaborn as sns
from statsmodels.graphics.gofplots import qqplot
!pip install scikit-uplift -q
from sklift.metrics import uplift_at_k, uplift_auc_score, qini_auc_score, weighted_average_uplift
from sklift.viz import plot_uplift_preds
from sklift.models import SoloModel, TwoModels
import xgboost as xgb


[33mWARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv[0m



# 读取csv文件，并将其存储在train变量中
train = pd.read_csv('../input/megafon-uplift-competition/train (1).csv')

我们看到了许多隐藏的特征X_1-X_50，二元处理（以对象格式）和二元转换



# 查看训练数据的前几行
train.head()

5 rows × 53 columns

# 对训练数据集进行信息描述
train.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 600000 entries, 0 to 599999
Data columns (total 53 columns):
 #   Column           Non-Null Count   Dtype  
---  ------           --------------   -----  
 0   id               600000 non-null  int64  
 1   treatment_group  600000 non-null  object 
 2   X_1              600000 non-null  float64
 3   X_2              600000 non-null  float64
 4   X_3              600000 non-null  float64
 5   X_4              600000 non-null  float64
 6   X_5              600000 non-null  float64
 7   X_6              600000 non-null  float64
 8   X_7              600000 non-null  float64
 9   X_8              600000 non-null  float64
 10  X_9              600000 non-null  float64
 11  X_10             600000 non-null  float64
 12  X_11             600000 non-null  float64
 13  X_12             600000 non-null  float64
 14  X_13             600000 non-null  float64
 15  X_14             600000 non-null  float64
 16  X_15             600000 non-null  float64
 17  X_16             600000 non-null  float64
 18  X_17             600000 non-null  float64
 19  X_18             600000 non-null  float64
 20  X_19             600000 non-null  float64
 21  X_20             600000 non-null  float64
 22  X_21             600000 non-null  float64
 23  X_22             600000 non-null  float64
 24  X_23             600000 non-null  float64
 25  X_24             600000 non-null  float64
 26  X_25             600000 non-null  float64
 27  X_26             600000 non-null  float64
 28  X_27             600000 non-null  float64
 29  X_28             600000 non-null  float64
 30  X_29             600000 non-null  float64
 31  X_30             600000 non-null  float64
 32  X_31             600000 non-null  float64
 33  X_32             600000 non-null  float64
 34  X_33             600000 non-null  float64
 35  X_34             600000 non-null  float64
 36  X_35             600000 non-null  float64
 37  X_36             600000 non-null  float64
 38  X_37             600000 non-null  float64
 39  X_38             600000 non-null  float64
 40  X_39             600000 non-null  float64
 41  X_40             600000 non-null  float64
 42  X_41             600000 non-null  float64
 43  X_42             600000 non-null  float64
 44  X_43             600000 non-null  float64
 45  X_44             600000 non-null  float64
 46  X_45             600000 non-null  float64
 47  X_46             600000 non-null  float64
 48  X_47             600000 non-null  float64
 49  X_48             600000 non-null  float64
 50  X_49             600000 non-null  float64
 51  X_50             600000 non-null  float64
 52  conversion       600000 non-null  int64  
dtypes: float64(50), int64(2), object(1)
memory usage: 242.6+ MB

特征没有标准化或归一化

# 使用describe()函数对训练数据集进行描述性统计分析
train.describe()

8 rows × 52 columns

然而，很有可能这些特征已经被清除。每个特征分布看起来都很正常。

# 给代码添加中文注释

# 设置行数和列数
rows, cols = 10, 5

# 创建一个包含多个子图的图形对象，并设置图形的大小
f, axs = plt.subplots(nrows=rows, ncols=cols, figsize=(20, 25))

# 设置图形的背景颜色为白色
f.set_facecolor("#fff")

# 设置特征数量为1
n_feat = 1

# 遍历每一行
for row in tqdm(range(rows)):
    # 遍历每一列
    for col in range(cols):
        try:
            # 绘制核密度估计图，并设置填充、透明度、线宽、边缘颜色等参数
            sns.kdeplot(x=f'X_{n_feat}', fill=True, alpha=1, linewidth=3, 
                        edgecolor="#264653", data=train, ax=axs[row, col], color='w')
            
            # 设置子图的背景颜色为深绿色，并设置透明度
            axs[row, col].patch.set_facecolor("#619b8a")
            axs[row, col].patch.set_alpha(0.8)
            
            # 设置子图的网格颜色和透明度
            axs[row, col].grid(color="#264653", alpha=1, axis="both")
        except IndexError: # 隐藏最后一个空图
            axs[row, col].set_visible(False)
        
        # 特征数量加1
        n_feat += 1

# 显示图形
f.show()

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模型系列：增益模型Uplift Modeling原理和案例-LMLPHP

只是为了确保，请看qq图。

# 设置子图的行数和列数
rows, cols = 10, 5

# 创建一个包含子图的图像对象
f, axs = plt.subplots(nrows=rows, ncols=cols, figsize=(20, 25))

# 设置图像的背景颜色为白色
f.set_facecolor("#fff")

# 设置特征数量为1
n_feat = 1

# 遍历每一行
for row in tqdm(range(rows)):
    # 遍历每一列
    for col in range(cols):
        try:
            # 绘制核密度估计图
            # sns.kdeplot(x=f'X_{n_feat}', fill=True, alpha=1, linewidth=3, 
            #             edgecolor="#264653", data=train, ax=axs[row, col], color='w')
            
            # 绘制QQ图
            qqplot(train[f'X_{n_feat}'], ax=axs[row, col], line='q')
            
            # 设置网格线的颜色为深绿色
            axs[row, col].grid(color="#264653", alpha=1, axis="both")
        
        # 如果索引超出范围，则隐藏最后一个空图
        except IndexError:
            axs[row, col].set_visible(False)
        
        # 特征数量加1
        n_feat += 1

# 显示图像
f.show()

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模型系列：增益模型Uplift Modeling原理和案例-LMLPHP

接下来让我们集中精力进行建模。

2. 指标

由于我们在研究之前没有Uplift，我们不能使用经典的Meta-Learners指标。然而，我们需要比较模型并了解它们的准确性。

1. Uplift@k
我们所需要做的就是对值进行排序（降序），并计算治疗组和对照组中目标变量（Y）的平均差异：
U p l i f t @ k = m e a n ( Y t r e a t m e n t @ k ) − m e a n ( Y c o n t r o l @ k ) Uplift@k = mean(Y^{treatment}@k) - mean(Y^{control}@k) Uplift@k=mean(Ytreatment@k)−mean(Ycontrol@k)
Y @ k Y@k Y@k - 前k%的目标变量

2. 按百分位数（十分位数）计算Uplift
相同的方法，但这里我们分别计算每个十分位数的差异
使用按百分位数计算的Uplift，我们可以计算加权平均Uplift：
加权平均Uplift$ = \frac{N^T_i * uplift_i}{\sum{N^T_i}} $
N i T N^T_i NiT​ - i百分位数中治疗组的大小

3. Uplift曲线和AUUC
Uplift曲线是一个依赖于对象数量的累积Uplift函数：
uplift curve i = ( Y t T N t T − Y t C N t C ) ( N t T + N t C ) \text{uplift curve}_i = (\frac{Y^T_t}{N^T_t}-\frac{Y^C_t}{N^C_t}) (N^T_t + N^C_t) uplift curvei​=(NtT​YtT​​−NtC​YtC​​)(NtT​+NtC​)
其中  t − 累积对象数量 , N − T和C组的大小 \text{其中 } t - \text{累积对象数量}, N - \text{T和C组的大小} 其中 t−累积对象数量,N−T和C组的大小

AUUC - Unplift曲线下的面积是随机Uplift曲线和模型曲线之间的面积，通过理想Uplift曲线下的面积进行归一化

4. Qini曲线和AUQC
Qini曲线是另一种累积函数的方法：
qini curve i = Y t T − Y t C N t T N t C \text{qini curve}_i = Y^T_t-\frac{Y^C_tN^T_t}{N^C_t} qini curvei​=YtT​−NtC​YtC​NtT​​

AUQC或Qini系数 - Qini曲线下的面积是随机Qini曲线和模型曲线之间的面积，通过理想Qini曲线下的面积进行归一化

train.columns

Index(['id', 'treatment_group', 'X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6',
       'X_7', 'X_8', 'X_9', 'X_10', 'X_11', 'X_12', 'X_13', 'X_14', 'X_15',
       'X_16', 'X_17', 'X_18', 'X_19', 'X_20', 'X_21', 'X_22', 'X_23', 'X_24',
       'X_25', 'X_26', 'X_27', 'X_28', 'X_29', 'X_30', 'X_31', 'X_32', 'X_33',
       'X_34', 'X_35', 'X_36', 'X_37', 'X_38', 'X_39', 'X_40', 'X_41', 'X_42',
       'X_43', 'X_44', 'X_45', 'X_46', 'X_47', 'X_48', 'X_49', 'X_50',
       'conversion'],
      dtype='object')

# 获取'treatment_group'列的唯一值
train['treatment_group'].unique()


array(['control', 'treatment'], dtype=object)

# 将'treatment_group'列中的值转换为0或1，如果值为'treatment'则转换为1，否则转换为0
train['treatment_group'] = train['treatment_group'].apply(lambda x: 1 if x=='treatment' else 0)

# 从sklearn库中导入train_test_split函数
from sklearn.model_selection import train_test_split

# 将train数据集的前100000行赋值给train变量
train = train[:100000]

# 从train数据集中选取名为'X_i'的特征列，其中i的取值范围为1到50，并将结果赋值给X变量
X = train[[f'X_{i}' for i in range(1, 51)]]

# 从train数据集中选取名为'treatment_group'的特征列，并将结果赋值给treatment变量
treatment = train['treatment_group']

# 从train数据集中选取名为'conversion'的特征列，并将结果赋值给y变量
y = train['conversion']

# 使用train_test_split函数将X、y和treatment按照指定的比例划分为训练集和验证集，并将划分结果分别赋值给X_train、X_val、y_train、y_val、treatment_train和treatment_val变量
X_train, X_val, y_train, y_val, treatment_train, treatment_val = train_test_split(X, y, treatment, test_size=0.2)

3. 元学习者

3.1 S-Learner

3.1 S-学习者

返回目录

S-learner的主要思想是使用特征、二进制处理（W）和二进制目标动作（Y）训练一个模型。然后使用常数W=1和W=0对测试数据进行预测。差异即为提升效果。

模型系列：增益模型Uplift Modeling原理和案例-LMLPHP

好消息是我们可以使用经典的机器学习分类器！让我们使用xgboost来做吧。你也可以尝试其他分类器并比较结果。

# 定义一个函数get_metrics，接受三个参数y_val, uplift, treatment_val
def get_metrics(y_val, uplift, treatment_val):
    # 计算指标

    # 计算前30%的提升值。按照组别排序控制组和处理组。整体排序。
    upliftk = uplift_at_k(y_true=y_val, uplift=uplift, treatment=treatment_val, strategy='by_group', k=0.3)
    upliftk_all = uplift_at_k(y_true=y_val, uplift=uplift, treatment=treatment_val, strategy='overall', k=0.3)

    # 计算Qini系数
    qini_coef = qini_auc_score(y_true=y_val, uplift=uplift, treatment=treatment_val)

    # 默认策略 - 整体排序
    # 计算提升曲线下面积
    uplift_auc = uplift_auc_score(y_true=y_val, uplift=uplift, treatment=treatment_val)
    # 计算加权平均提升值
    wau = weighted_average_uplift(y_true=y_val, uplift=uplift, treatment=treatment_val, strategy='by_group')
    wau_all = weighted_average_uplift(y_true=y_val, uplift=uplift, treatment=treatment_val)

    # 打印结果
    print(f'uplift at top 30% by group: {upliftk:.2f} by overall: {upliftk_all:.2f}\n',
          f'Weighted average uplift by group: {wau:.2f} by overall: {wau_all:.2f}\n',
          f'AUUC by group: {uplift_auc:.2f}\n',
          f'AUQC by group: {qini_coef:.2f}\n')
    
    # 返回一个包含指标结果的字典
    return {'uplift@30': upliftk, 'uplift@30_all': upliftk_all, 'AUQC': qini_coef, 'AUUC': uplift_auc, 
            'WAU': wau, 'WAU_all': wau_all}

# 创建一个XGBoost分类器模型，设置随机种子为42，目标函数为二元逻辑回归，禁用标签编码
xgb_sm = xgb.XGBClassifier(random_state=42, objective='binary:logistic', use_label_encoder=False)

# 创建一个SoloModel对象，使用上面创建的XGBoost分类器模型作为估计器
sm = SoloModel(estimator=xgb_sm)

# 使用训练数据集X_train、y_train和treatment_train来拟合SoloModel模型
sm = sm.fit(X_train, y_train, treatment_train, estimator_fit_params={})

# 使用拟合好的SoloModel模型对验证数据集X_val进行预测
uplift_sm = sm.predict(X_val)

# 使用get_metrics函数计算验证数据集的评估指标，包括y_val、uplift_sm和treatment_val
res = get_metrics(y_val, uplift_sm, treatment_val)

[12:14:57] WARNING: ../src/learner.cc:1115: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.
uplift at top 30% by group: 0.18 by overall: 0.18
 Weighted average uplift by group: 0.04 by overall: 0.04
 AUUC by group: 0.15
 AUQC by group: 0.21

3.2 T-Learner

3.2 T学习器

跳转到目录

T-learner的主要思想是训练两个独立的模型：一个基于治疗后的观察数据（T），另一个基于对照组数据（C）。提升效果是模型T和模型C在数据上的预测差异。

模型系列：增益模型Uplift Modeling原理和案例-LMLPHP



# 初始化两个xgboost分类器，分别用于处理treatment组和control组
xgb_T = xgb.XGBClassifier(random_state=42, objective='binary:logistic', use_label_encoder=False)
xgb_C = xgb.XGBClassifier(random_state=42, objective='binary:logistic', use_label_encoder=False)

# 初始化TwoModels类，将treatment组和control组的分类器传入
sm = TwoModels(estimator_trmnt=xgb_T, estimator_ctrl=xgb_C)

# 使用训练数据拟合模型
sm = sm.fit(X_train, y_train, treatment_train, estimator_trmnt_fit_params={}, estimator_ctrl_fit_params={})

# 对验证集进行预测
uplift_sm = sm.predict(X_val)

# 计算模型的评估指标
res = get_metrics(y_val, uplift_sm, treatment_val)

[12:15:47] WARNING: ../src/learner.cc:1115: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.
[12:16:11] WARNING: ../src/learner.cc:1115: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.
uplift at top 30% by group: 0.17 by overall: 0.17
 Weighted average uplift by group: 0.04 by overall: 0.04
 AUUC by group: 0.13
 AUQC by group: 0.18

结果比S-learner稍差。

3.3 T-Learner依赖模型

T-learner与依赖模型的主要思想是使用相反模型的预测（概率）来训练T或C模型。
这种方法是从分类器链方法中采用的：https://scikit-learn.org/stable/auto_examples/multioutput/plot_classifier_chain_yeast.html

模型系列：增益模型Uplift Modeling原理和案例-LMLPHP

这种方法有两种可能的实现方式：基于C模型中的T-probs和基于T模型中的C-probs：

  1. u p l i f t i = P T ( x i , P C ( X ) ) − P C ( x i ) uplift_i = P^T(x_i, P^C(X)) - P^C(x_i) uplifti​=PT(xi​,PC(X))−PC(xi​)
  2. u p l i f t i = P T ( x i ) − P C ( x i , P T ( x i ) ) uplift_i = P^T(x_i) - P^C(x_i, P^T(x_i)) uplifti​=PT(xi​)−PC(xi​,PT(xi​))

第一种方法：


# 创建两个XGBClassifier对象，分别作为treatment模型和control模型
xgb_T = xgb.XGBClassifier(random_state=42, objective='binary:logistic', use_label_encoder=False)
xgb_C = xgb.XGBClassifier(random_state=42, objective='binary:logistic', use_label_encoder=False)

# 创建TwoModels对象，将treatment模型和control模型传入，并指定方法为'ddr_control'
sm = TwoModels(estimator_trmnt=xgb_T, estimator_ctrl=xgb_C, method='ddr_control')

# 使用训练数据拟合TwoModels对象
sm = sm.fit(X_train, y_train, treatment_train, estimator_trmnt_fit_params={}, estimator_ctrl_fit_params={})

# 使用拟合好的TwoModels对象对验证数据进行预测
uplift_sm = sm.predict(X_val)

# 使用预测结果和验证数据计算评估指标
res = get_metrics(y_val, uplift_sm, treatment_val)

[12:16:37] WARNING: ../src/learner.cc:1115: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.
[12:17:02] WARNING: ../src/learner.cc:1115: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.
uplift at top 30% by group: 0.17 by overall: 0.17
 Weighted average uplift by group: 0.04 by overall: 0.04
 AUUC by group: 0.12
 AUQC by group: 0.18

第二种方法：


# 创建两个XGBoost分类器，用于处理treatment组和control组
xgb_T = xgb.XGBClassifier(random_state=42, objective='binary:logistic', use_label_encoder=False)
xgb_C = xgb.XGBClassifier(random_state=42, objective='binary:logistic', use_label_encoder=False)

# 创建TwoModels对象，使用xgb_T和xgb_C作为估计器，并选择ddr_treatment方法
sm = TwoModels(estimator_trmnt=xgb_T, estimator_ctrl=xgb_C, method='ddr_treatment')

# 使用训练数据拟合TwoModels对象
sm = sm.fit(X_train, y_train, treatment_train, estimator_trmnt_fit_params={}, estimator_ctrl_fit_params={})

# 对验证数据进行预测
uplift_sm = sm.predict(X_val)

# 计算模型的评估指标
res = get_metrics(y_val, uplift_sm, treatment_val)

[12:17:27] WARNING: ../src/learner.cc:1115: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.
[12:17:51] WARNING: ../src/learner.cc:1115: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.
uplift at top 30% by group: 0.17 by overall: 0.17
 Weighted average uplift by group: 0.04 by overall: 0.04
 AUUC by group: 0.13
 AUQC by group: 0.19

参考资料：
https://www.uplift-modeling.com/en/latest/

12-29 04:29
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