Parameter Inference via Differentiable Diffusion Bridge Importance Sampling

TL;DR

This paper presents a differentiable, score matching-based framework for parameter inference in high-dimensional diffusion processes, enabling insights into biological evolution and relationships with stable numerical methods.

Contribution

It introduces a novel, numerically stable method combining score matching and importance sampling for parameter inference in complex diffusion models.

Findings

Successfully applied to biological morphometry data

Enables gradient-based optimization of diffusion parameters

Provides accurate ancestral state reconstructions

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.