Statistical Inference and Stability Boundaries of Multi-cellular Interaction Hypergraphs from Asynchronous Event Streams

2026-05-26

AI Summary

This study addresses the challenge of inferring higher-order interactions in multicellular systems from asynchronous event streams by proposing the Hyperedge-Triggered Hawkes (HTH) process. The model captures group-wise co-activation dynamics through a hyperedge-based intensity term that explicitly represents higher-order interactions. To enable efficient parameter estimation, the authors develop a closed-form EM algorithm augmented with a piecewise compensator to eliminate integration bias and employ CP tensor decomposition to reduce the hyperedge parameter complexity from O(N^K) to O(NR). Theoretical analysis reveals a systematic −22% bias in hyperedge weight estimation that depends non-monotonically on the kernel decay rate. Experiments demonstrate that the method achieves pairwise recovery errors below 5% across 11 synthetic datasets and yields a +20.6 nat improvement in log-likelihood over pairwise baselines on recordings from mouse retinal ganglion cells.

Abstract

We introduce the Hyperedge-triggered Hawkes (HTH) process for inferring higher-order interaction structure in multi-cellular systems from asynchronous event-time data. Beyond standard pairwise excitation, the HTH intensity includes a term activated by the simultaneous co-firing of a cell group within a temporal window. We derive a closed-form Expectation-Maximisation algorithm whose key ingredient is a piecewise compensator that eliminates the systematic bias present in the naive integral formulation. A CP tensor decomposition reduces the hyperedge parameter count from O(N^K) to O(NR). Across eleven synthetic experiments the framework achieves pairwise recovery error below 5%, while revealing a systematic -22% bias on hyperedge weights that is non-monotonic in the kernel decay rate, ruling out a simple temporal-overlap explanation and motivating adaptive kernel methods. On multi-electrode recordings of mouse retinal ganglion cells, the model yields a +20.6 nat likelihood gain over the pairwise baseline, providing suggestive but not decisive evidence for higher-order interactions. Code and all experiments are publicly available at https://github.com/Hanii0210/hypergraph-hawkes.

Problem

• higher-order interactions
• multi-cellular systems
• asynchronous event streams
• hypergraph inference
• statistical inference

Innovation

• Hyperedge-triggered Hawkes process
• higher-order interactions
• Expectation-Maximisation algorithm
• CP tensor decomposition
• asynchronous event streams