Latent confounding in high-dimensional nonlinear models

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Wang, Yuhao, Shah, Rajen
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908482434760704
author Wang, Yuhao
Shah, Rajen
author_facet Wang, Yuhao
Shah, Rajen
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_06274
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Latent confounding in high-dimensional nonlinear models
Wang, Yuhao
Shah, Rajen
Statistics Theory
Methodology
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.
title Latent confounding in high-dimensional nonlinear models
topic Statistics Theory
Methodology
url https://arxiv.org/abs/2508.06274