Learning Higher-Order Interactions from Incomplete Spatiotemporal Data with Mixtures of Hypergraph Laplacians

The paper introduces MoHL, a mixture of hypergraph Laplacians that learns group-wise relational structure directly from incomplete spatiotemporal traffic sensor data. MoHL discovers overlapping sensor groups, constructs a Laplacian component for each interaction order, and learns their mixture through holdouts that mimic missingness patterns, sharing weights across group-induced couplings to pool evidence. Experiments on three traffic networks show that MoHL achieves the lowest error under day-long gaps, with far fewer learned parameters than deep imputers, demonstrating the benefit of higher-order groups and shared weights when relational evidence is scarce.

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