Parameter Inference via Differentiable Diffusion Bridge Importance Sampling

2024/11/13 by Nicklas Boserup, Gefan Yang, Boserup, Nicklas +7 · 1 citation
Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2411.08993

openalex publication_date 2024/11/13 · openalex created_date 2024/11/17 · openalex updated_date 2026/07/28

Abstract

We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including ancestral state reconstruction. Estimation is performed by utilising score matching to approximate diffusion bridges, which are subsequently used in an importance sampler to estimate log-likelihoods. The entire setup is differentiable, allowing gradient ascent on approximated log-likelihoods. This allows both parameter inference and diffusion mean estimation. This novel, numerically stable, score matching-based parameter inference framework is presented and demonstrated on biological two- and three-dimensional morphometry data.

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