Spectral Representation for Causal Estimation with Hidden Confounders

TL;DR

This paper introduces a spectral method using singular value decomposition and saddle-point optimization for causal effect estimation in the presence of hidden confounders, improving accuracy over existing techniques.

Contribution

It proposes a novel spectral representation approach combined with saddle-point optimization for causal inference with hidden confounders, extending existing methods with neural network generalizations.

Findings

Outperforms existing methods on benchmark datasets

Effective in both instrumental variable regression and proxy causal learning

Avoids double sampling bias through saddle-point formulation

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 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.