Causal Representation Meets Stochastic Modeling under Generic Geometry
This work addresses a bottleneck in causal representation learning for real-world continuous-time data, enabling applications in fields like genomics and neuroscience.
The paper tackles the problem of learning identifiable causal representations from continuous-time stochastic processes, such as point processes, by developing a method called MUTATE that achieves identifiability and effectively answers scientific questions in genomics and neuroscience.
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.