Representation Balancing with Decomposed Patterns for Treatment Effect Estimation

Yiyan HUANG, WANG Siyi, Cheuk Hang LEUNG, Qi WU, Dongdong WANG, Zhixiang Huang

Keywords: Treatment Effect Estimation, Counterfactual Estimation, Representation Balancing, Selection Bias, Covariate Shift

TL;DR: We derive the bound for individual propensity confusion and decompose representation balancing into patterns of (i) individual propensity confusion and group distance minimization and (ii) pre-balancing and balancing, for treatment effect estimation.

Abstract: Estimating treatment effects from observational data is subject to a problem of covariate shift caused by selection bias. Recent studies have attempted to mitigate this problem by group distance minimization, that is, balancing the distribution of representations between the treated and controlled groups. The rationale behind this is that learning balanced representations while preserving the predictive power of factual outcomes is expected to generalize to counterfactual inference. Inspired by this, we propose a new approach to better capture the patterns that contribute to representation balancing and outcome prediction. Specifically, we derive a theoretical bound that naturally ties the notion of propensity confusion to representation balancing, and further transform the balancing Patterns into Decompositions of Individual propensity confusion and Group distance minimization (PDIG). Moreover, we propose to decompose proxy features into Patterns of Pre-balancing and Balancing Representations (PPBR), as it is insufficient if only balanced representations are considered in outcome prediction. Extensive experiments on simulation and benchmark data confirm not only PDIG leads to mutual reinforcement between individual propensity confusion and group distance minimization, but also PPBR brings improvement to outcome prediction, especially counterfactual inference. We believe these findings are heuristics for further investigation of what affects the generalizability of representation balancing models in counterfactual estimation.

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