Adaptive, Robust and Scalable Bayesian Filtering for Online Learning

• URL: http://arxiv.org/abs/2505.07267v1
• Date: Mon, 12 May 2025 06:40:29 GMT
• Title: Adaptive, Robust and Scalable Bayesian Filtering for Online Learning
• Authors: Gerardo Duran-Martin,
• Abstract summary: We introduce Bayesian filtering as a principled framework for tackling diverse sequential machine learning problems.<n>This thesis addresses key challenges in applying Bayesian filtering to these problems: adaptivity to non-stationary environments, to model misspecifications and outliers, and scalability to the high-dimensional parameter space of deep neural networks.<n>We develop novel tools within the Bayesian filtering framework to address each of these challenges, including: (i) a modular framework that enables the development adaptive approaches for online learning; (ii) a novel, provably robust filter with similar computational cost to standard filters, that employs Generalised Bayes; and (
• Score: 0.5439020425819
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this thesis, we introduce Bayesian filtering as a principled framework for tackling diverse sequential machine learning problems, including online (continual) learning, prequential (one-step-ahead) forecasting, and contextual bandits. To this end, this thesis addresses key challenges in applying Bayesian filtering to these problems: adaptivity to non-stationary environments, robustness to model misspecification and outliers, and scalability to the high-dimensional parameter space of deep neural networks. We develop novel tools within the Bayesian filtering framework to address each of these challenges, including: (i) a modular framework that enables the development adaptive approaches for online learning; (ii) a novel, provably robust filter with similar computational cost to standard filters, that employs Generalised Bayes; and (iii) a set of tools for sequentially updating model parameters using approximate second-order optimisation methods that exploit the overparametrisation of high-dimensional parametric models such as neural networks. Theoretical analysis and empirical results demonstrate the improved performance of our methods in dynamic, high-dimensional, and misspecified models.

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