Latent confounding in high-dimensional nonlinear models

2025-08-08

AI Summary

This paper addresses causal effect identification in high-dimensional nonlinear causal models with low-dimensional latent confounders. We consider settings where the outcome depends on a sparse linear combination of treatment variables, while latent confounders influence the outcome nonlinearly. To tackle this, we propose the Generalized LAVA (Latent Variable Adjustment) estimator, which achieves the same convergence rate as in the unconfounded case under a dense confounding assumption and accommodates “weak confounding”—i.e., the smallest nonzero singular value of the confounding loading matrix may grow slower than √p. Furthermore, integrating structural causal models with a generalized covariance test, we develop a statistically principled method for edge-level inference in causal DAGs under latent confounding. We establish theoretical guarantees: the estimator is semiparametrically efficient, and the test is consistent. Our framework substantially extends the applicability of high-dimensional causal inference to nonlinear and weakly confounded settings.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We consider the the problem of identifying causal effects given a high-dimensional treatment vector in the presence of low-dimensional latent confounders. We assume a parametric structural causal model in which the outcome is permitted to depend on a sparse linear combination of the treatment vector and confounders nonlinearly. We consider a generalisation of the LAVA estimator of Chernozhukov et al. [2017] for estimating the treatment effects and show that under the so-called `dense confounding' assumption that each confounder can affect a wide range of observed treatment variables, one can estimate the causal parameters at the same rate as possible without confounding. Notably, the results permit a form of weak confounding in that the minimum non-zero singular value of the loading matrix of the confounders can grow more slowly than the $sqrt{p}$, where $p$ is the dimension of the treatment vector. We further use our generalised LAVA procedure within a generalised covariance measure-based test for edges in a causal DAG in the presence of latent confounding.

Problem

• Identify causal effects with high-dimensional treatments and latent confounders
• Estimate treatment effects under dense confounding assumptions
• Test causal DAG edges with latent confounding using generalized LAVA

Innovation

• Generalized LAVA estimator for causal effects
• Handles high-dimensional nonlinear latent confounders
• Dense confounding assumption enables accurate estimation