Latent confounding in high-dimensional nonlinear models

TL;DR

This paper develops a method for estimating causal effects in high-dimensional nonlinear models with latent confounders, showing that under certain conditions, confounding can be effectively mitigated even with weak confounding effects.

Contribution

It generalizes the LAVA estimator to high-dimensional nonlinear models with latent confounders, allowing consistent causal inference under dense confounding assumptions.

Findings

Causal parameters can be estimated at optimal rates under dense confounding.

The method tolerates weak confounding where confounder effects grow slowly with treatment dimension.

The approach enables causal DAG edge testing in high-dimensional settings with latent confounders.

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.