Causal Representation Meets Stochastic Modeling under Generic Geometry

TL;DR

This paper introduces a method for learning causal representations from continuous-time stochastic processes, enabling scientific insights in fields like genomics and neuroscience.

Contribution

It develops an identifiable variational autoencoder framework for continuous-time stochastic processes, addressing a gap in existing causal representation learning methods.

Findings

MUTATE effectively infers stochastic dynamics in simulated data.

It uncovers causal mechanisms in genomics and neuroscience.

The approach demonstrates practical utility in real-world scientific questions.

Abstract

Learning meaningful causal representations from observations has emerged as a crucial task for facilitating machine learning applications and driving scientific discoveries in fields such as climate science, biology, and physics. This process involves disentangling high-level latent variables and their causal relationships from low-level observations. Previous work in this area that achieves identifiability typically focuses on cases where the observations are either i.i.d. or follow a latent discrete-time process. Nevertheless, many real-world settings require identifying latent variables that are continuous-time stochastic processes (e.g., multivariate point processes). To this end, we develop identifiable causal representation learning for continuous-time latent stochastic point processes. We study its identifiability by analyzing the geometry of the parameter space. Furthermore, we develop MUTATE, an identifiable variational autoencoder framework with a time-adaptive transition module to infer stochastic dynamics. Across simulated and empirical studies, we find that MUTATE can effectively answer scientific questions, such as the accumulation of mutations in genomics and the mechanisms driving neuron spike triggers in response to time-varying dynamics.