Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounders

TL;DR

This paper introduces a method to estimate effects of multiple interventions with hidden confounders using both observational and single-variable intervention data, leveraging nonlinear causal models.

Contribution

It provides identifiability results and a joint likelihood-based estimation approach for nonlinear causal effects with hidden confounders, validated through experiments.

Findings

Successful identifiability under nonlinear Gaussian noise models

Effective estimation of joint effects from combined data regimes

Outperforms baseline methods on synthetic and real data

Abstract

We propose an approach to estimate the effect of multiple simultaneous interventions in the presence of hidden confounders. To overcome the problem of hidden confounding, we consider the setting where we have access to not only the observational data but also sets of single-variable interventions in which each of the treatment variables is intervened on separately. We prove identifiability under the assumption that the data is generated from a nonlinear continuous structural causal model with additive Gaussian noise. In addition, we propose a simple parameter estimation method by pooling all the data from different regimes and jointly maximizing the combined likelihood. We also conduct comprehensive experiments to verify the identifiability result as well as to compare the performance of our approach against a baseline on both synthetic and real-world data.