Learning Latent Causal Dynamics
This work addresses the challenge of distribution shifts in time-series modeling, which is critical for applications like forecasting and control, though it appears incremental as it builds on existing causal inference methods.
The authors tackled the problem of learning and correcting time-series models under unknown distribution shifts by proposing LiLY, a framework that recovers time-delayed latent causal variables and identifies their relations, enabling efficient model correction with few samples from new environments.
One critical challenge of time-series modeling is how to learn and quickly correct the model under unknown distribution shifts. In this work, we propose a principled framework, called LiLY, to first recover time-delayed latent causal variables and identify their relations from measured temporal data under different distribution shifts. The correction step is then formulated as learning the low-dimensional change factors with a few samples from the new environment, leveraging the identified causal structure. Specifically, the framework factorizes unknown distribution shifts into transition distribution changes caused by fixed dynamics and time-varying latent causal relations, and by global changes in observation. We establish the identifiability theories of nonparametric latent causal dynamics from their nonlinear mixtures under fixed dynamics and under changes. Through experiments, we show that time-delayed latent causal influences are reliably identified from observed variables under different distribution changes. By exploiting this modular representation of changes, we can efficiently learn to correct the model under unknown distribution shifts with only a few samples.