Causal Representation Learning with Instantaneous and Lagged Relations via Nonstationarity

2026-10-02

AI Summary

This study addresses the challenges of jointly modeling instantaneous and lagged causal relationships and handling non-stationarity in time series data by proposing the iCReN framework. Leveraging non-stationarity, the method establishes identifiability conditions for latent states through contrastive learning combined with discrete or continuous auxiliary variables. This approach yields the first unified identifiability theory for both instantaneous and lagged causal structures, thereby overcoming key limitations of existing methods. Experimental results demonstrate that the proposed framework accurately recovers underlying causal structures on synthetic datasets and substantially enhances downstream predictive performance on real-world data.

Abstract

Causal representation learning for time-series data aims to identify latent states and their causal relations from observations. In this setting, an important challenge is to model both lagged causal relations across observation intervals and faster causal effects that appear as instantaneous relations within an interval, while accounting for nonstationarity in time-series data. However, methods that jointly handle these causal relations and nonstationarity remain limited. To address this gap, we establish sufficient conditions for identifying latent states up to component permutation and component-wise invertible transformations, and their instantaneous and lagged causal structures up to the same permutation, using an observed auxiliary variable, such as time or a condition label, associated with changes in transition-noise distributions. Based on these results, we propose iCReN, a framework that uses contrastive learning with discrete or continuous auxiliary variables to learn latent representations and estimate their instantaneous and lagged causal structures. Experiments demonstrate accurate recovery of latent states and both instantaneous and lagged causal structures on synthetic data and the utility of the learned representations for downstream forecasting on real-world data.

Problem

• Causal Representation Learning
• Time-Series Data
• Instantaneous and Lagged Relations
• Nonstationarity

Innovation

• Causal Representation Learning
• Instantaneous and Lagged Relations
• Nonstationarity
• Identifiability
• Contrastive Learning