## S-Learner

Tags: #machine learning #causual inference### Equation

$$\mu(x,w)=\mathbb{E}[Y_{i}|X=x_{i},W=w] \\ \hat{\tau}(x)=\hat{\mu}(x,1)-\hat{\mu}(x,0)$$### Latex Code

\mu(x,w)=\mathbb{E}[Y_{i}|X=x_{i},W=w] \\ \hat{\tau}(x)=\hat{\mu}(x,1)-\hat{\mu}(x,0)

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### Introduction

#### Equation

#### Latex Code

\mu(x,w)=\mathbb{E}[Y_{i}|X=x_{i},W=w] \\ \hat{\tau}(x)=\hat{\mu}(x,1)-\hat{\mu}(x,0)

#### Explanation

S-Learner use a single machine learning estimator \mu(x,w) to estimate outcome Y directly. And the treatment assigment variable W=0,1 is treated as features of S-learner models. The CATE estimation is calculated as the difference between two outputs given the same model \mu and different inputs features of W, namely w=1 and w=0.

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