Spectral Representation for Causal Estimation with Hidden Confounders

2024-07-15

arXiv.org

AI Summary

This paper addresses causal effect estimation under latent confounding, focusing on two key settings: instrumental variable regression with observed confounders and proxy-variable-based causal learning. We propose a novel spectral representation framework grounded in the spectral decomposition of conditional expectation operators. For the first time, we jointly leverage saddle-point optimization and neural function approximation for latent-confounder-robust causal inference, thereby circumventing the double-sampling bias inherent in conventional approaches. Our method avoids explicit modeling of high-dimensional nonlinear structures while ensuring both theoretical interpretability and computational tractability. Extensive experiments across multiple benchmark datasets demonstrate that our approach significantly outperforms state-of-the-art methods—particularly in finite-sample regimes and complex functional spaces—achieving superior robustness and estimation accuracy.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Estimating causal effects with hidden confounders.
• Using spectral methods for instrumental variable regression.
• Avoiding double sampling bias via saddle-point optimization.

Innovation

• SVD for causal estimation with hidden confounders
• Saddle-point optimization avoids double sampling bias
• Neural net generalization of IV regression