arXiv：cs.LG· Isaias Banales, Arturo Jaramillo·· 4 小时前
基于投影 Wasserstein-Fisher-Rao 流的 Hawkes 过程背景强度估计
Projected Wasserstein-Fisher-Rao Flows for Hawkes Background-Intensity Estimation
AI 导读
研究在触发机制已知时估计 Hawkes 过程背景强度的问题，将背景视为具有正则密度的未知有限正测度，提出基于 Wasserstein-Fisher-Rao 几何的似然变分方法。
正文
Abstract:We consider the problem of estimating the background intensity of a Hawkes process when the triggering mechanism is known, treating the background as an unknown finite positive measure with a regular density. We propose a likelihood-based variational approach based on the Wasserstein-Fisher-Rao geometry. In this setting, the relevant first variations are naturally distribution-valued and therefore fall outside the classical gradient-flow formulation. We develop a distributional framework for the resulting dynamics and give them a finite-dimensional meaning through projections onto statistical manifolds. We identify the true background as the unique zero of a limiting generalized gradient and, under suitable stability, compactness, integrability and approximation conditions, establish a conditional consistency theorem for measurable estimators satisfying the empirical projected equations on events whose probabilities tend to one. Finally, we specialize the construction to Gaussian-mixture manifolds and obtain an explicit finite-dimensional scheme.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.19588 [stat.ML] |
| (or arXiv:2610.19588v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.19588 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Arturo Jaramillo [view email]
[v1]
Wed, 14 Oct 2026 04:59:27 UTC (1,383 KB)
来源：arXiv：cs.LG · arxiv.org