Statistical Inference and Stability Boundaries of Multi-cellular Interaction Hypergraphs from Asynchronous Event Streams
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916047199666176 |
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| author | Xu, Zihan |
| author_facet | Xu, Zihan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_26608 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Statistical Inference and Stability Boundaries of Multi-cellular Interaction Hypergraphs from Asynchronous Event Streams Xu, Zihan Methodology 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. |
| title | Statistical Inference and Stability Boundaries of Multi-cellular Interaction Hypergraphs from Asynchronous Event Streams |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.26608 |