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Residual TPP: A Unified Lightweight Approach for Event Stream Data Analysis

ICML 2025 · Time series › Causal and generative time series · approach: Generative temporal point processes

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Proposes Residual TPP, which fits a Hawkes process, uses a weight-based Residual Events Decomposition (RED) to isolate poorly fit residual events, and trains an arbitrary neural TPP only on those residuals.

Problem

Neural TPPs are computationally expensive on long event sequences while classical TPPs such as the Hawkes process are too rigid and fail on outliers and complex dynamics; no decomposition method analogous to time-series STD exists for event streams.

Approach

A weight function derived from the integrated intensity of a fitted Hawkes process (with an influence function whose derivative is unbiased under Exp(1)) separates events well captured by the statistical model from residual events; a neural TPP is trained only on residuals and superposed with the Hawkes intensity via a mixing weight alpha equal to the residual fraction.

Key results

• Residual TPP variants improve log-likelihood over their neural TPP baselines on all six datasets, e.g., RES NHP reaches -1.825 vs NHP -2.031 on MIMIC-II and -0.712 vs -2.613 on Earthquake.
• Residual TPP lowers time RMSE on most datasets, e.g., RES RMTPP 0.504 vs RMTPP 0.613 on Amazon, and reduces type error (RES ODETPP 19.2% vs ODETPP 22.1% on MIMIC-II).
• End-to-end training time is lower for every Residual TPP than its baseline, e.g., RES ATTNHP 657.5s vs ATTNHP 1093s on Volcano and 5646s vs 6375s on Amazon.

Measured effects reported in the paper

Surprising findings

• Residual TPP improves over baselines even on synthetic data where the true process is not a Hawkes process, which the authors interpret as RED being agnostic to the data-generating process.
• Some alternative influence-function variants (RES THP NEW, RES ATTNHP NEW) underperform the original on MIMIC-II log-likelihood, showing sensitivity to the choice of influence function.

Limitations

• Periodic baseline is not modeled in the experiments; the Hawkes component uses a fixed constant baseline.
• Hyperparameters a, b, and the residual threshold w are tuned per dataset, and the paper notes the choice affects the proportion of residual events.
• Theoretical unbiasedness holds asymptotically only when there is no event contamination and T goes to infinity, with rho1 = rho2.

Experimental setup

Datasets: MIMIC-II Retweet Earthquake StackOverflow Amazon Volcano

Benchmarks: MIMIC-II Retweet Earthquake StackOverflow Amazon Volcano

Metrics: test log-likelihood next-event time RMSE next-event type error rate end-to-end training time

Baselines: MHP RMTPP NHP SAHP THP AttNHP ODETPP FullyNN

Builds on: Hawkes process EasyTPP Seasonal-Trend Decomposition Zhang et al. 2025 unbiased weighting for event outliers

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