用可微分扩散桥实现高维非线性过程的参数推断
Parameter Inference via Differentiable Diffusion Bridge Importance Sampling
- 基于分数匹配构建可微分的扩散桥
- 在生物形态数据上成功估计参数与均值
- 适合需要精确推断的演化生物学研究
我们提出一种高维非线性扩散过程的参数推断方法。通过分数匹配近似扩散桥，并将其用于重要性采样以估计对数似然。整个框架可微分，支持对近似对数似然进行梯度上升，从而实现参数推断与扩散均值估计。该新型数值稳定的方法在生物二维和三维形态学数据上得到验证。
原文摘要 · Abstract (English)
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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