Causal Representation Meets Stochastic Modeling under Generic Geometry

2026-02-04

AI Summary

This work addresses the challenge of causal identifiability in continuous-time stochastic point processes with latent variables by proposing MUTATE, a novel framework that achieves, for the first time, identifiable representation learning of high-dimensional continuous-time latent variables and their causal mechanisms. Built upon a variational autoencoder architecture, MUTATE integrates a time-adaptive transition module with geometric analysis in parameter space to effectively disentangle dynamically evolving latent factors from low-dimensional observations. Experiments on both synthetic and real-world data—including gene mutation accumulation trajectories and neuronal spike trains—demonstrate that MUTATE not only accurately recovers the underlying causal structure but also offers strong scientific interpretability, thereby establishing a new paradigm for continuous-time latent causal modeling.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• causal representation
• continuous-time stochastic processes
• identifiability
• latent variables
• point processes

Innovation

• causal representation learning
• continuous-time stochastic processes
• identifiability
• variational autoencoder
• point processes