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MOCHA: Discovering Multi-Order Dynamic Causal Structure in Temporal Point Processes

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Latent-variable causal estimation

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Proposes MOCHA, a neural temporal point process whose intensity sums multi-hop path influences over a learned time-varying DAG, trained end-to-end with acyclicity and sparsity penalties, and evaluated on seven clinical and social event datasets.

Problem

Existing neural temporal point process models capture only first-order or static dependencies among event types, which misses multi-order and time-varying causal structure and limits interpretability.

Approach

Decomposes the TPP intensity into first- and multi-order components by summing multi-hop path products over a learned time-varying DAG (weights from a GAT over type and time-interval embeddings), with NOTEARS-style acyclicity and l1 sparsity penalties so the learned graph is interpretable.

Key results

• MOCHA reports the lowest NLL on all seven datasets, e.g., 0.69 on CAD and 0.70 on SE, versus best baselines ITHP/THP.
• Ablation shows NLL on AKI dropping from 5.88 (univariate Hawkes) to 3.80 with the full model.
• Average matching rate for first-order clinical causal paths to AKI Phase III is 92.10%, with Sodium Low -> Anion Gap High -> Phase III at 99.39%.

Surprising findings

• Reported NLL values are negative on TB (-0.36) and SO-ablation-level comparisons, and MOCHA's SO NLL (2.32) is not lower than the ITHP-free baselines' best in all cases, i.e., NLL on SO is not clearly best versus NHP (2.67) only marginally.

Limitations

• Ground-truth causal paths are based on clinical guidelines and only 10 AKI paths, with matching rate evaluation limited to one disease.
• The acyclicity and sparsity constraints are soft regularizers, so DAG validity is not strictly guaranteed.
• Hyperparameters such as the maximum order L, threshold theta and beta are fixed without a reported sensitivity analysis.

Experimental setup

Datasets: AKI CAD SE ST RT TB SO MIMIC-IV

Benchmarks: AKI CAD SE ST RT TB SO

Metrics: negative log-likelihood RMSE accuracy causal path matching rate

Baselines: RMTPP NHP SAHP THP AttNHP HCLTPP ITHP NJDTPP

Builds on: Hawkes process NOTEARS Transformer sinusoidal positional encoding Graph Attention Network

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