Bayesian learning: Challenges, limitations and pragmatics

Heide, R. de (2021)

Doctoral Thesis

This dissertation is about Bayesian learning from data. How can humans and computers learn from data? This question is at the core of both statistics and — as its name already suggests — machine learning. Bayesian methods are widely used in these fields, yet they have certain limitations and problems of interpretation. In two chapters of this dissertation, we examine such a limitation, and overcome it by extending the standard Bayesian framework. In two other chapters, we discuss how different philosophical interpretations of Bayesianism affect mathematical definitions and theorems about Bayesian methods and their use in practise. While some researchers see the Bayesian framework as normative (all statistics should be based on Bayesian methods), in the two remaining chapters, we apply Bayesian methods in a pragmatic way: merely as tool for interesting learning problems (that could also have been addressed by non-Bayesian methods).

• Bayesian learning
• Hypothesis testing
• Optional stopping
• Bayes factors
• Generalized Bayes
• Best-arm identification
• E-values

• All authors: Heide, R. de
• Supervisor: Grünwald, P.D.; Meulman, J.J.
• Co-supervisor: Koolen, W.M.
• Committee: Eliel, E.R.; Luijk, R.M. van; Carpentier, A.; Ramdas, A.; Roy, D.M.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute (MI), Faculty of Science, Leiden University
• Date: 2021-01-26
• Sponsorship: The author’s PhD position at the Mathematical Institute was supported by the Leiden IBM-SPSS Fund. The research was performed at the Centrum Wiskunde & Informatica (CWI). Part of the work was done while the author was visiting Inria Lille, partly funded by Leids Universiteits Fonds / Drs. J.R.D. Kuikenga Fonds voor Mathematici travel grant number W19204-1-35.