Learning Temporally Causal Latent Processes from General Temporal Data
This addresses the challenge of unsupervised causal discovery in temporal data for researchers in machine learning and causality, though it appears incremental as it builds on existing VAEs with new conditions.
The paper tackles the problem of recovering time-delayed latent causal variables from measured temporal data, proposing LEAP, a framework that extends VAEs with constraints to identify these processes, and shows it considerably outperforms baselines in experiments.
Our goal is to recover time-delayed latent causal variables and identify their relations from measured temporal data. Estimating causally-related latent variables from observations is particularly challenging as the latent variables are not uniquely recoverable in the most general case. In this work, we consider both a nonparametric, nonstationary setting and a parametric setting for the latent processes and propose two provable conditions under which temporally causal latent processes can be identified from their nonlinear mixtures. We propose LEAP, a theoretically-grounded framework that extends Variational AutoEncoders (VAEs) by enforcing our conditions through proper constraints in causal process prior. Experimental results on various datasets demonstrate that temporally causal latent processes are reliably identified from observed variables under different dependency structures and that our approach considerably outperforms baselines that do not properly leverage history or nonstationarity information. This demonstrates that using temporal information to learn latent processes from their invertible nonlinear mixtures in an unsupervised manner, for which we believe our work is one of the first, seems promising even without sparsity or minimality assumptions.