DistCUTS: Distribution-Aware Causal Discovery from Incomplete Multivariate Time Series

Discovering causal relationships from incomplete multivariate time series is challenging because missing observations obscure temporal dependencies. Existing approaches typically address this challenge by alternating between missing-value reconstruction and causal graph learning. However, their structure-learning objectives primarily assess whether a source variable’s history improves point predictions of a target’s future values. As a result, they may overlook causal edges whose effects manifest primarily in the target’s conditional variability rather than its conditional mean, yielding incomplete causal structures. Omitting these edges can further impair missing-value reconstruction by excluding relevant causal information, with the resulting errors propagating into subsequent graph estimation. To address this limitation, we propose DistCUTS, a distribution-aware framework that complements point prediction with history-conditioned residual distribution matching to capture both mean-driven and scale-driven dependencies. Specifically, DistCUTS estimates history-dependent residual scales from graph-constrained source histories and uses these scales to parameterize conditional residual distributions. A maximum mean discrepancy (MMD) objective compares samples from these distributions with the corresponding observed residuals, encouraging the model to capture residual variability supported by the observations. As auxiliary components, we demean observed residuals to reduce sensitivity to predicted-mean offsets and use the learned residual scales to guide missing-value reconstruction. Experiments on synthetic and real-world datasets demonstrate that DistCUTS outperforms the evaluated baselines.