Causal Heteroscedastic Structure Learning From Incomplete Temporal data

Abdellah Rahmani, Pascal Frossard

Discovering causal structures in multivariate time series (MTS) is critical in domains such as finance and neuroscience, yet remains challenging in practice due to three distinct obstacles. First, MTS are routinely corrupted by missing values, where naive impute-then-discover pipelines distort the underlying data distribution and yield spurious causal graphs. Second, identifying instantaneous effects is difficult even on complete data, and missingness further entangles imputation with graph recovery. Third, real-world data frequently exhibits heteroscedastic noise with variance driven by both instantaneous and lagged causes, violating the core assumptions of standard discovery methods. Existing approaches fail to address these challenges concurrently, typically presuming complete data, homoscedastic noise, or strictly time-lagged relationships. Crucially, we show through ablation studies that resolving these issues sequentially, rather than jointly, leads to a substantial degradation in performance. To overcome this, we introduce Cheesefill, an optimal transport framework for causal structure learning under missingness and heteroscedastic noise. Cheesefill parameterizes causal…