元学习器

元学习器是一种估计模型，旨在当处理手段为离散变量时通过机器学习模型去评估CATE。治疗方案为离散变量的意思也就是当无混淆条件下非1即0。通常来讲，它利用多个可灵活选择的机器学习模型。

YLearn 实现了3个元学习器: S-Learner, T-Learner, and X-Learner.

示例

import numpy as np
from numpy.random import multivariate_normal

from sklearn.ensemble import RandomForestClassifier, GradientBoostingRegressor

import matplotlib.pyplot as plt

from ylearn.estimator_model.meta_learner import SLearner, TLearner, XLearner
from ylearn.estimator_model.doubly_robust import DoublyRobust
from ylearn.exp_dataset.exp_data import binary_data
from ylearn.utils import to_df

# build the dataset
d = 5
n = 2500
n_test = 250

y, x, w = binary_data(n=n, d=d, n_test=n_test)
data = to_df(outcome=y, treatment=x, w=w)
outcome = 'outcome'
treatment = 'treatment'
adjustment = data.columns[2:]

# build the test dataset
treatment_effect = lambda x: (1 if x[1] > 0.1 else 0) * 8

w_test = multivariate_normal(np.zeros(d), np.diag(np.ones(d)), n_test)
delta = 6/n_test
w_test[:, 1] = np.arange(-3, 3, delta)

SLearner

s = SLearner(model=GradientBoostingRegressor())
s.fit(data=data, outcome=outcome, treatment=treatment, adjustment=adjustment) # training
s_pred = s.estimate(data=test_data, quantity=None) # predicting

TLearner

t = TLearner(model=GradientBoostingRegressor())
t.fit(data=data, outcome=outcome, treatment=treatment, adjustment=adjustment) # training
t_pred = t.estimate(data=test_data, quantity=None) # predicting

XLearner

x = XLearner(model=GradientBoostingRegressor())
x.fit(data=data, outcome=outcome, treatment=treatment, adjustment=adjustment) # training
x_pred = x.estimate(data=test_data, quantity=None) # predicting

S-Learner

SLearner 采用一个机器学习模型来评估因果效应。具体来说，我们用机器学习模型 \(f\) 从治疗方案 \(x\) 和调整集 (或者协变量) \(w\) 中拟合一个模型去预测结果 \(y\):

\[y = f(x, w).\]

因果效应 \(\tau(w)\) 被计算为:

\[\tau(w) = f(x=1, w) - f(x=0, w).\]

class ylearn.estimator_model.meta_learner.SLearner(model, random_state=2022, is_discrete_treatment=True, categories='auto', *args, **kwargs)

参数:

• model (estimator, optional) – The base machine learning model for training SLearner. Any model should be some valid machine learning model with fit() and predict() functions.

• random_state (int, default=2022) –

• is_discrete_treatment (bool, default=True) – Treatment must be discrete for SLearner.

• categories (str, optional, default='auto') –

fit(data, outcome, treatment, adjustment=None, covariate=None, treat=None, control=None, combined_treatment=True, **kwargs)

Fit the SLearner in the dataset.

参数:

• data (pandas.DataFrame) – Training dataset for training the estimator.

• outcome (list of str, optional) – Names of the outcome.

• treatment (list of str, optional) – Names of the treatment.

• adjustment (list of str, optional, default=None) – Names of the adjustment set ensuring the unconfoundness,

• covariate (list of str, optional, default=None) – Names of the covariate.

• treat (int, optional) – Label of the intended treatment group

• control (int, optional) – Label of the intended control group

• combined_treatment (bool, optional, default=True) –

  Only modify this parameter for multiple treatments, where multiple discrete treatments are combined to give a single new group of discrete treatment if set as True. When combined_treatment is set to True, then if there are multiple treatments, we can use the combined_treatment technique to covert the multiple discrete classification tasks into a single discrete classification task. For an example, if there are two different binary treatments:

  1. treatment_1: \(x_1 | x_1 \in \{'sleep', 'run'\}\),

  2. treatment_2: \(x_2 | x_2 \in \{'study', 'work'\}\),

  then we can convert these two binary classification tasks into a single classification task with 4 different classes:

  treatment: \(x | x \in \{0, 1, 2, 3\}\),

  where, for example, 1 stands for (‘sleep’ and ‘stuy’).

返回:

The fitted instance of SLearner.

返回类型:

instance of SLearner

estimate(data=None, quantity=None)

Estimate the causal effect with the type of the quantity.

参数:

• data (pandas.DataFrame, optional, default=None) – Test data. The model will use the training data if set as None.

• quantity (str, optional, default=None) –

  Option for returned estimation result. The possible values of quantity include:

  1. ’CATE’ : the estimator will evaluate the CATE;

  2. ’ATE’ : the estimator will evaluate the ATE;

  3. None : the estimator will evaluate the ITE or CITE.

返回:

The estimated causal effects

返回类型:

ndarray

effect_nji(data=None)

Calculate causal effects with different treatment values.

返回:

Causal effects with different treatment values.

返回类型:

ndarray

_comp_transormer(x, categories='auto')

Transform the discrete treatment into one-hot vectors properly.

参数:

• x (numpy.ndarray, shape (n, x_d)) – An array containing the information of the treatment variables.

• categories (str or list, optional, default='auto') –

返回:

The transformed one-hot vectors.

返回类型:

numpy.ndarray

T-Learner

TLearner的问题是当调整集向量为多维时治疗方案向量仅为一维。因此，如果调整集的维度超过1，那么评估结果将总是逼近于0。 TLearner用两个机器学习模型去评估因果效应。具体来讲，令 \(w\) 为调整集（或协变量），我们

1. 分别拟合两个模型 \(f_t(w)\) 对于治疗组 (\(x=\) treat) 和 \(f_0(w)\) 对于控制组 (\(x=\) control):

   \[y_t = f_t(w)\]

其中, \(x=\) treat.

\[y_0 = f_0(w)\]

其中, \(x=\) control.

2. 计算因果效应 \(\tau(w)\) 作为两个模型预测结果的差异:

   \[\tau(w) = f_t(w) - f_0(w).\]

class ylearn.estimator_model.meta_learner.TLearner(model, random_state=2022, is_discrete_treatment=True, categories='auto', *args, **kwargs)

参数:

• model (estimator, optional) – The base machine learning model for training TLearner. Any model should be some valid machine learning model with fit() and predict() functions.

• random_state (int, default=2022) –

• is_discrete_treatment (bool, default=True) – Treatment must be discrete for SLearner.

• categories (str, optional, default='auto') –

fit(data, outcome, treatment, adjustment=None, covariate=None, treat=None, control=None, combined_treatment=True, **kwargs)

Fit the SLearner in the dataset.

参数:

• data (pandas.DataFrame) – Training dataset for training the estimator.

• outcome (list of str, optional) – Names of the outcome.

• treatment (list of str, optional) – Names of the treatment.

• adjustment (list of str, optional, default=None) – Names of the adjustment set ensuring the unconfoundness,

• covariate (list of str, optional, default=None) – Names of the covariate.

• treat (int, optional) – Label of the intended treatment group

• control (int, optional) – Label of the intended control group

• combined_treatment (bool, optional, default=True) –

  Only modify this parameter for multiple treatments, where multiple discrete treatments are combined to give a single new group of discrete treatment if set as True. When combined_treatment is set to True, then if there are multiple treatments, we can use the combined_treatment technique to covert the multiple discrete classification tasks into a single discrete classification task. For an example, if there are two different binary treatments:

  1. treatment_1: \(x_1 | x_1 \in \{'sleep', 'run'\}\),

  2. treatment_2: \(x_2 | x_2 \in \{'study', 'work'\}\),

  then we can convert these two binary classification tasks into a single classification task with 4 different classes:

  treatment: \(x | x \in \{0, 1, 2, 3\}\),

  where, for example, 1 stands for (‘sleep’ and ‘stuy’).

返回:

The fitted instance of TLearner.

返回类型:

instance of TLearner

estimate(data=None, quantity=None)

Estimate the causal effect with the type of the quantity.

参数:

• data (pandas.DataFrame, optional, default=None) – Test data. The model will use the training data if set as None.

• quantity (str, optional, default=None) –

  Option for returned estimation result. The possible values of quantity include:

  1. ’CATE’ : the estimator will evaluate the CATE;

  2. ’ATE’ : the estimator will evaluate the ATE;

  3. None : the estimator will evaluate the ITE or CITE.

返回:

The estimated causal effects

返回类型:

ndarray

effect_nji(data=None)

Calculate causal effects with different treatment values.

返回:

Causal effects with different treatment values.

返回类型:

ndarray

_comp_transormer(x, categories='auto')

Transform the discrete treatment into one-hot vectors properly.

参数:

• x (numpy.ndarray, shape (n, x_d)) – An array containing the information of the treatment variables.

• categories (str or list, optional, default='auto') –

返回:

The transformed one-hot vectors.

返回类型:

numpy.ndarray

X-Learner

TLearner未能完全有效地利用数据，XLearner可以解决这个问题。训练一个XLearner可以分为3步:

1. 与TLearner类似, 我们首先分别训练两个不同的模型对于控制组和治疗组:

   \[\begin{split}& f_0(w) \text{for the control group}\\ & f_1(w) \text{for the treat group}.\end{split}\]

2. 生成两个新数据集 \(\{(h_0, w)\}\) 用控制组, :math:`{(h_1, w)}`用治疗组。 其中

   \[\begin{split}h_0 & = f_1(w) - y_0,\\ h_1 & = y_1 - f_0(w).\end{split}\]

   然后，训练两个机器学习模型在这些数据集中 \(k_0(w)\) 和 \(k_1(w)\)

   \[\begin{split}h_0 & = k_0(w) \\ h_1 & = k_1(w).\end{split}\]

3. 结合以上两个模型得到最终的模型:

   \[g(w) = k_0(w)a(w) + k_1(w)(1 - a(w))\]

   其中, \(a(w)\) 是一个调整 \(k_0\) 和 \(k_1\) 的权重调整系数。

最后, 因果效应 \(\tau(w)\) 通过以下方式评估:

\[\tau(w) = g(w).\]

class ylearn.estimator_model.meta_learner.XLearner(model, random_state=2022, is_discrete_treatment=True, categories='auto', *args, **kwargs)

参数:

• model (estimator, optional) – The base machine learning model for training SLearner. Any model should be some valid machine learning model with fit() and predict() functions.

• random_state (int, default=2022) –

• is_discrete_treatment (bool, default=True) – Treatment must be discrete for SLearner.

• categories (str, optional, default='auto') –

fit(data, outcome, treatment, adjustment=None, covariate=None, treat=None, control=None, combined_treatment=True, **kwargs)

Fit the SLearner in the dataset.

参数:

• data (pandas.DataFrame) – Training dataset for training the estimator.

• outcome (list of str, optional) – Names of the outcome.

• treatment (list of str, optional) – Names of the treatment.

• adjustment (list of str, optional, default=None) – Names of the adjustment set ensuring the unconfoundness,

• covariate (list of str, optional, default=None) – Names of the covariate.

• treat (int, optional) – Label of the intended treatment group

• control (int, optional) – Label of the intended control group

• combined_treatment (bool, optional, default=True) –

  Only modify this parameter for multiple treatments, where multiple discrete treatments are combined to give a single new group of discrete treatment if set as True. When combined_treatment is set to True, then if there are multiple treatments, we can use the combined_treatment technique to covert the multiple discrete classification tasks into a single discrete classification task. For an example, if there are two different binary treatments:

  1. treatment_1: \(x_1 | x_1 \in \{'sleep', 'run'\}\),

  2. treatment_2: \(x_2 | x_2 \in \{'study', 'work'\}\),

  then we can convert these two binary classification tasks into a single classification task with 4 different classes:

  treatment: \(x | x \in \{0, 1, 2, 3\}\),

  where, for example, 1 stands for (‘sleep’ and ‘stuy’).

返回:

The fitted instance of XLearner.

返回类型:

instance of XLearner

estimate(data=None, quantity=None)

Estimate the causal effect with the type of the quantity.

参数:

• data (pandas.DataFrame, optional, default=None) – Test data. The model will use the training data if set as None.

• quantity (str, optional, default=None) –

  Option for returned estimation result. The possible values of quantity include:

  1. ’CATE’ : the estimator will evaluate the CATE;

  2. ’ATE’ : the estimator will evaluate the ATE;

  3. None : the estimator will evaluate the ITE or CITE.

返回:

The estimated causal effects

返回类型:

ndarray

effect_nji(data=None)

Calculate causal effects with different treatment values.

返回:

Causal effects with different treatment values.

返回类型:

ndarray

_comp_transormer(x, categories='auto')

Transform the discrete treatment into one-hot vectors properly.

参数:

• x (numpy.ndarray, shape (n, x_d)) – An array containing the information of the treatment variables.

• categories (str or list, optional, default='auto') –

返回:

The transformed one-hot vectors.

返回类型:

numpy.ndarray