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.

翻译：我们提出了一种在高维非线性扩散过程中进行参数推断的方法。我们阐述了该方法在获取物种演化及其相互关系（包括祖先状态重建）方面的适用性。估计过程通过利用分数匹配来近似扩散桥实现，这些扩散桥随后被用于重要性采样器中以估计对数似然。整个框架具有可微性，允许对近似对数似然执行梯度上升。这使得参数推断和扩散均值估计均能实现。本文提出并展示了这一新颖、数值稳定的基于分数匹配的参数推断框架，并在生物二维和三维形态测量数据上进行了验证。