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Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events
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Proposes ARCH, a hierarchical flow-matching model that generates event time and then location, computes conditional intensities via ODE log-density and CDF invariance, and uses hybrid masking for arbitrary conditioned inference on spatiotemporal events.
Problem
Spatiotemporal point process models either impose strong structural assumptions (Poisson/Hawkes) or use expressive generative models that lose tractable conditional intensities, and they are mostly limited to autoregressive next-event prediction rather than inverse inference, trajectory recovery, or
Approach
Factor the joint event distribution into a temporal flow and a spatial flow conditioned on time, compute the conditional intensity via a log-density ODE and a CDF-invariance lemma, and train a single transformer encoder-decoder with autoregressive, random-condition, and consecutive masks so one model handles many conditional inference tasks.
Key results
- On STSC-SYN, ARCH achieves relative L2 intensity error 0.370 vs 0.588 for AutoSTPP and 0.918 for DeepSTPP.
- Next-event prediction on Earthquake: ARCH spatial error 6.55 vs DSTPP 6.77; on COVID-19 spatial 0.391 vs 0.419.
- Inverse inference of first event on Earthquake: ARCH spatial 7.34 vs best KNNImpute 10.1 (k=10).
Surprising findings
- Joint multi-step forecasting by ARCH is not uniformly better than DSTPP; on COVID-19 temporal error ARCH (0.071) is slightly worse than DSTPP (0.070) at length 5.
- For missing-event recovery on COVID-19, ARCH's temporal error is slightly worse than KNNImpute at some missing ratios.
Limitations
- Assumes the number of target events or attributes is specified in advance; cannot infer how many events are missing or how many will occur.
- Structural priors for interpretability are not incorporated.
- Does not handle discrete event-mask (type) generation.
Experimental setup
Datasets: Earthquake COVID-19 Citibike STHP-SYN STSC-SYN
Benchmarks: Earthquake COVID-19 Citibike STHP-SYN STSC-SYN
Metrics: RMSE Euclidean distance relative L2 error
Baselines: DeepSTPP AutoSTPP NSTPP DSTPP NJSDE STHP HPP KNNImpute ARCH-AR
Builds on: flow matching neural spatiotemporal point process DSTPP DeepSTPP AutoSTPP
Closest papers by meaning
- Seahorse: A Unified Benchmarking Framework for Spatiotemporal Event Modeling (NeurIPS 2026 · similarity 0.89)
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- SCENT: Robust Spatiotemporal Learning for Continuous Scientific Data via Scalable Conditioned Neural Fields (ICML 2025 · similarity 0.85)
- Wavelet-Driven Spatiotemporal Predictive Learning: Bridging Frequency and Time Variations (AAAI 2024 · similarity 0.85)
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