Reproduce “Learning Temporally Causal Latent Processes from General Temporal Data” on OpenResearch

About this paper

Weiran Yao, Yuewen Sun, Alex Ho, Changyin Sun, Kun Zhang

This work introduces theoretical identifiability conditions for learning time-delayed latent causal processes from their nonlinear mixtures in observed temporal data, moving beyond restrictive assumptions like linearity or independent sources. A deep generative model, LEAP, is developed to implement these conditions, demonstrating high accuracy in recovering latent factors and their causal graphs on synthetic data (e.g., 0.98 MCC) and extracting interpretable causal dynamics from real-world video and motion data.

Key insights

• Latent, temporally causal processes, even when nonlinearly mixed, can be uniquely identified by exploiting nonstationarity (via auxiliary variables modulating noise) or specific non-Gaussian noise distributions (e.g., generalized Laplacian for parametric models).
• The 'Independent Noise' condition, crucial for causal inference, can be enforced in the latent space by learning inverse causal transition functions and factorizing noise distributions via contrastive learning.
• A deep generative model framework, specifically a Variational AutoEncoder (VAE) with a tailored causal process prior, can practically realize these theoretical identifiability conditions for unsupervised latent causal discovery.

Summary by alphaXiv.