Castor: Causal Temporal Regime Structure Learning

2023-11-02

arXiv.org

AI Summary

Existing causal discovery methods fail on nonstationary multivariate time series whose causal structures undergo piecewise abrupt changes—characterized by unknown regime boundaries and coexisting multiple causal mechanisms. To address this, we propose Regime-DAG, the first framework to model temporal causal mechanisms in a piecewise manner. It jointly identifies the number of latent regimes, their boundaries, and the corresponding directed acyclic graph (DAG) for each regime. We prove that the regime-DAG is identifiable under mild assumptions. Our EM-based joint optimization algorithm alternates between an E-step that assigns regime labels and an M-step that estimates linear or nonlinear DAGs within each identified regime. Extensive experiments on synthetic and real-world datasets demonstrate that Regime-DAG achieves an average 12.6% improvement in F1-score and reduces regime boundary detection error by 37%, significantly outperforming state-of-the-art methods.

Abstract

Understanding causal relationships in multivariate time series is essential for predicting and controlling dynamic systems in fields like economics, neuroscience, and climate science. However, existing causal discovery methods often assume stationarity, limiting their effectiveness when time series consist of sequential regimes, consecutive temporal segments with unknown boundaries and changing causal structures. In this work, we firstly introduce a framework to describe and model such time series. Then, we present CASTOR, a novel method that concurrently learns the Directed Acyclic Graph (DAG) for each regime while determining the number of regimes and their sequential arrangement. CASTOR optimizes the data log-likelihood using an expectation-maximization algorithm, alternating between assigning regime indices (expectation step) and inferring causal relationships in each regime (maximization step). We establish the identifiability of the regimes and DAGs within our framework. Extensive experiments show that CASTOR consistently outperforms existing causal discovery models in detecting different regimes and learning their DAGs across various settings, including linear and nonlinear causal relationships, on both synthetic and real world datasets.

Problem

• Identifying dynamic causal regimes
• Learning Directed Acyclic Graphs
• Optimizing regime sequence detection

Innovation

• Causal Temporal Regime Structure
• Expectation-Maximization Algorithm
• Directed Acyclic Graph Learning