Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises

TL;DR

FANTOM is a novel framework for causal discovery in multivariate time series that effectively handles non-stationarity, non-Gaussian, and heteroscedastic noise, while identifying regime shifts and causal structures.

Contribution

It introduces FANTOM, a unified Bayesian EM-based method that infers regimes, their causal graphs, and handles complex noise distributions, with proven identifiability.

Findings

FANTOM outperforms existing methods on synthetic data.

It accurately detects regime shifts and causal structures.

Theoretical proof of identifiability under mild assumptions.

Abstract

Understanding causal relationships in multivariate time series is crucial in many scenarios, such as those dealing with financial or neurological data. Many such time series exhibit multiple regimes, i.e., consecutive temporal segments with a priori unknown boundaries, with each regime having its own causal structure. Inferring causal dependencies and regime shifts is critical for analyzing the underlying processes. However, causal structure learning in this setting is challenging due to (1) non-stationarity, i.e., each regime can have its own causal graph and mixing function, and (2) complex noise distributions, which may be nonGaussian or heteroscedastic. Existing causal discovery approaches cannot address these challenges, since generally assume stationarity or Gaussian noise with constant variance. Hence, we introduce FANTOM, a unified framework for causal discovery that handles non-stationary processes along with non-Gaussian and heteroscedastic noises. FANTOM simultaneously infers the number of regimes and their corresponding indices and learns each regime's Directed Acyclic Graph. It uses a Bayesian Expectation Maximization algorithm that maximizes the evidence lower bound of the data log-likelihood. On the theoretical side, we prove, under mild assumptions, that temporal heteroscedastic causal models, introduced in FANTOM's formulation, are identifiable in both stationary and non-stationary settings. In addition, extensive experiments on synthetic and real data show that FANTOM outperforms existing methods.