ReTimeCausal: EM-Augmented Additive Noise Models for Interpretable Causal Discovery in Irregular Time Series

This paper studies causal discovery in irregularly sampled time series-a pivotal challenge in high-stakes domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal mechanisms. Traditional methods (e.g., Granger causality, PCMCI) fail to reconcile multi-scale interactions (e.g., hourly storms vs. decadal climate shifts), while neural approaches (e.g., CUTS+) lack interpretability, stemming from a critical gap: existing frameworks either rigidly assume temporal regularity or aggregate dynamics into opaque representations, neglecting real-world granularity and auditable logic. To bridge this gap, we propose ReTimeCausal, a novel integration of Additive Noise Models (ANM) and Expectation-Maximization (EM) that unifies physics-guided data imputation with sparse causal inference. Through kernelized sparse regression and structural constraints, ReTimeCausal iteratively refines missing values (E-step) and causal graphs (M-step), resolving cross-frequency dependencies and missing data issues. Extensive experiments on synthetic and real-world datasets demonstrate that ReTimeCausal outperforms existing state-of-the-art methods under challenging irregular sampling and missing data conditions.