LIST OF FIGURES xvii 5.1 Illustrative example of the misalignment between underlying factors and observed distributions. . . . . . . . . . . . . . . . . . . . 107 5.2 Example images of Square, Arrow, dSprites, and 3D Shapes. . . . 110 5.3 Visualisation of OOD splits for datasets with 2 factors. . . . . . . 111 5.4 Mean negative ELBOs for all datasets and models. . . . . . . . . . 116 5.5 Differences between train and OOD ELBO for all datasets and models. ................................117 5.6 Examples of training and OOD samples (top lines) and their reconstructions (bottom lines) by two different models, for the Arrow0.625split............................117 5.7 OOD detection example for LSBD-VAE on the Arrow 0.25 split. . . 118 5.8 AUROC scores for detecting OOD from train data, for all datasets andmodels...............................119 5.9 LSBD-VAE reconstructions of OOD data from various splits of dSprites (left) and 3D Shapes (right). . . . . . . . . . . . . . . . . 120 5.10 DLSBD scores (lower is better) for various OOD splits. . . . . . . 121 5.11 2D latent embeddings (top) and latent traversals (bottom) for LSBD-VAE trained on Arrow for increasingly large OOD splits, visualised on a flattened 2D torus. . . . . . . . . . . . . . . . . . . 122
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