Introduction to Bayesian ML/DL, with Application to Parameter Inference of Coupled Non-linear ODEs – Part 2

In this talk, the speaker will present introductory materials about Bayesian Machine Learning.

Abstract
The problem of approximating the posterior distribution (or density estimation in general) is a crucial problem in Bayesian statistics, in which intractable integrals often become the computational bottleneck. MCMC sampling is the most widely used family of algorithms for approximating posteriors. However, if the underlying graphical model is too complex or the data is in very high dimensions, then such sampling-based methodologies run into several problems. Variational inference (Jordan et al., 1999; Wainwright and Jordan, 2008) is a family of machine learning methodologies that transforms the problem of approximating posterior densities to an optimization, which lets us circumvent all such problems. In the first part, I will introduce the general framework of variational inference and some underlying theory, accompanied by an illustrative example of LDA (Blei et al., 2003). In the second part, I will introduce some recent works on applying variational inference to parameter inference of coupled non-linear ODEs arising in various biological contexts.