Causal Inference for Latent Outcomes Learned with Factor Models

TL;DR

This paper introduces a novel method for causal inference on latent outcomes derived from high-dimensional data using factor models, addressing interference issues and providing theoretical guarantees and practical tools.

Contribution

It is the first to formally address causal inference on latent outcomes in the context of factor models, proposing a new algorithm with theoretical guarantees and practical implementation.

Findings

Proposed algorithm effectively estimates causal effects on latent outcomes.

Theoretical guarantees ensure estimator consistency.

Method demonstrates utility in simulation and cancer data analysis.

Abstract

In many fields$\unicode{x2013}$including genomics, epidemiology, natural language processing, social and behavioral sciences, and economics$\unicode{x2013}$it is increasingly important to address causal questions in the context of factor models or representation learning. In this work, we investigate causal effects on $\textit{latent outcomes}$ derived from high-dimensional observed data using nonnegative matrix factorization. To the best of our knowledge, this is the first study to formally address causal inference in this setting. A central challenge is that estimating a latent factor model can cause an individual's learned latent outcome to depend on other individuals' treatments, thereby violating the standard causal inference assumption of no interference. We formalize this issue as $\textit{learning-induced interference}$ and distinguish it from interference present in a data-generating process. To address this, we propose a novel, intuitive, and theoretically grounded algorithm to estimate causal effects on latent outcomes while mitigating learning-induced interference and improving estimation efficiency. We establish theoretical guarantees for the consistency of our estimator and demonstrate its practical utility through simulation studies and an application to cancer mutational signature analysis. All baseline and proposed methods are available in our open-source R package, ${\tt causalLFO}$.