Transfer Causal Learning: Causal Effect Estimation with Knowledge Transfer

A novel problem of improving causal effect estimation accuracy with the help of knowledge transfer under the same covariate (or feature) space setting, i.e., homogeneous transfer learning (TL), is studied, referred to as the Transfer Causal Learning (TCL) problem. While most recent efforts in adapting TL techniques to estimate average causal effect (ACE) have been focused on the heterogeneous covariate space setting, those methods are inadequate for tackling the TCL problem since their algorithm designs are based on the decomposition into shared and domain-specific covariate spaces. To address this issue, we propose a generic framework called $\ell_1$-TCL, which incorporates $\ell_1$ regularized TL for nuisance parameter estimation and downstream plug-in ACE estimators, including outcome regression, inverse probability weighted, and doubly robust estimators. Most importantly, with the help of Lasso for high-dimensional regression, we establish non-asymptotic recovery guarantees for the generalized linear model (GLM) under the sparsity assumption for the proposed $\ell_1$-TCL. From an empirical perspective, $\ell_1$-TCL is a generic learning framework that can incorporate not only GLM but also many recently developed non-parametric methods, which can enhance robustness to model mis-specification. We demonstrate this empirical benefit through extensive numerical simulation by incorporating both GLM and recent neural network-based approaches in $\ell_1$-TCL, which shows improved performance compared with existing TL approaches for ACE estimation. Furthermore, our $\ell_1$-TCL framework is subsequently applied to a real study, revealing that vasopressor therapy could prevent 28-day mortality within septic patients, which all baseline approaches fail to show.