Spectral Representation for Causal Estimation with Hidden Confounders

Tongzheng Ren, Haotian Sun, Antoine Moulin, Arthur Gretton, Bo Dai

Keywords: causal inference, representation learning

TL;DR: We propose a method for estimating causal effects by leveraging the spectral representation of some conditional expectation operator and solving a saddle-point optimization problem for instrumental variable regression and proxy causal learning.

Abstract: We address the problem of causal effect estimation where hidden confounders are present, with a focus on two settings: instrumental variable regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator, followed by a saddle-point optimization problem, which, in the context of IV regression, can be thought of as a neural net generalization of the seminal approach due to Darolles et al. (2011). Saddle-point formulations have gathered considerable attention recently, as they can avoid the infamous double sampling bias and are amenable to modern function approximation methods. We provide experimental validation in various settings, and show that our approach outperforms existing methods on common benchmarks.

Submission Number: 29