On Probabilistic Machine Learning – From Score-Based Sampling to Variational Population Models

Abstract:

Probabilistic machine learning provides a principled framework for representing uncertainty in complex models. However, exact Bayesian inference is rarely tractable in modern machine learning due to high-dimensional latent spaces, nonlinear model structures, and intractable probability distributions. As a result, practical probabilistic modelling relies on approximate inference methods.

This work investigates two complementary approaches to approximate inference in probabilistic models where exact Bayesian inference is intractable. The first contribution develops an empirical Bayes variational autoencoder framework for population modelling, combining latent-variable inference with neural ordinary differential equations. The second contribution develops a Markov chain Monte Carlo correction framework for score-based diffusion models, enabling sampling-based corrections without requiring an explicit energy function.

Although these contributions arise in different application domains, they address a common challenge: how uncertainty can be represented, inferred, and utilised when exact Bayesian inference becomes infeasible. Together, the works illustrate how optimisation-based and sampling-based inference can be used to construct scalable probabilistic machine learning methods for dynamical and generative modelling.

Discussion leader is Johan Alenlöv, Linköpings Universitet

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