Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises
Abdellah Rahmani, Pascal Frossard
Understanding causal relationships in multivariate time series is crucial in many scenarios, such as financial and neurological data. Many such time series exhibit multiple regimes, i.e., consecutive segments with unknown boundaries. Each regime has its own causal structure. Detecting these causal dependencies and regime shifts is critical for revealing regime indices and 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 non-Gaussian or heteroscedastic, with variance depending on one or more influencing variables. Existing causal discovery approaches often assume stationarity or Gaussian noise with constant variance. To address these challenges, We introduce FANTOM, a unified framework that tackles non-stationarity along with non-Gaussian and heteroscedastic noises. FANTOM simultaneously learns each regime’s Directed Acyclic Graph (DAG) and infers the number and indices of these regimes, using a Bayesian Expectation Maximization algorithm that maximizes the evidence lower bound of the data log likelihood. On the theoretical side, we prove, under common assumptions, that temporal heteroscedastic causal models are identifiable in both stationary and non-stationary settings. In addition, extensive experiments on synthetic and real data show that FANTOM outperforms existing methods.