Learning Latent Causal Dynamics

TL;DR

This paper introduces LiLY, a framework for identifying latent causal variables and their relations in time-series data, enabling efficient model correction under distribution shifts with minimal samples.

Contribution

LiLY is the first method to recover time-delayed latent causal dynamics and their changes from observed data under distribution shifts, with proven identifiability.

Findings

Successfully identified latent causal influences under different shifts.

Efficient correction of models with few new samples.

Established theoretical identifiability of causal dynamics.

Abstract

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.