Contents Summary v List of Publications ix List of Figures xv List of Tables xix 1 Introduction 1 1.1 Motivation............................... 1 1.2 ResearchQuestions.......................... 5 1.2.1 Anomaly Detection with Probabilistic Generative Models . 5 1.2.2 Quantifying and Learning Linear Symmetry-Based Disentanglement(LSBD)...................... 6 1.2.3 Out-of-Distribution Generalisation with Linear SymmetryBased Disentangled Representations . . . . . . . . . . . . 7 1.3 Thesis Outline and Contributions . . . . . . . . . . . . . . . . . . 9 2 Background 11 2.1 VariationalAutoencoders. . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Disentanglement ........................... 15 2.3 GroupTheory............................. 18 2.4 MeasureTheory............................ 20
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