Parameter Inference via Differentiable Diffusion Bridge Importance Sampling
This provides a method for parameter inference in diffusion models, applicable to evolutionary biology for species analysis, but appears incremental as it combines existing techniques like score matching and importance sampling.
The authors tackled parameter inference in high-dimensional, non-linear diffusion processes, introducing a differentiable framework using score matching and importance sampling, and demonstrated it on biological morphometry data.
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.