Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events

TL;DR

This paper introduces ARCH, a hierarchical flow model for complex spatiotemporal event distributions that supports diverse inference tasks with high accuracy.

Contribution

ARCH is a novel hierarchical flow framework enabling flexible conditioning and unified inference for spatiotemporal event modeling.

Findings

ARCH outperforms existing baselines in prediction tasks.

ARCH effectively supports inverse inference and trajectory recovery.

Experiments on synthetic and real data validate ARCH's versatility.

Abstract

Events in spatiotemporal systems are ubiquitous, yet modeling their complex distributions remains challenging. Existing point process models often rely on strong structural assumptions and are typically limited to autoregressive, event-by-event prediction. As a result, they struggle to support broader inference tasks such as inverse inference, trajectory reconstruction, and recovery of missing event locations. We introduce Arbitrarily Conditioned Hierarchical Flows (ARCH), a hierarchical flow matching framework for spatiotemporal event modeling. ARCH is expressive enough to capture complex event distributions while enabling tractable and accurate computation of conditional intensities, which quantify instantaneous event risk. Built on a history-encoder-generative-decoder architecture, ARCH introduces a hybrid masking strategy for flexible conditioning on arbitrary observed events. This enables a unified treatment of forecasting, inverse inference, and partial trajectory recovery within a single framework. Experiments on synthetic and real-world datasets show that ARCH consistently outperforms existing baselines across both prediction and conditional inference tasks.