Summary Deep learning models excel at solving pattern recognition tasks by learning from high-dimensional data. Discriminative models, which predict low-dimensional labels from the data observations, have been successful but discard valuable information about underlying real-world mechanisms. To counter this, generative modelling and representation learning aim to model such real-world mechanisms, by learning how to generate new data or find lower-dimensional representations that capture its complexity. In this thesis, we focus in particular on the Variational Autoencoder (VAE), a probabilistic generative model that learns latent representations of observed data. A key motivation for learning representations is their usefulness for downstream tasks. One example is anomaly detection, which is often achieved by assigning an anomaly score to datapoints. Negative likelihood assigned by a VAE trained on normal data forms a natural candidate for such an anomaly score. This entails that datapoints are considered anomalous if they cannot be represented well by the VAE. If the VAE’s representations accurately model the underlying real-world properties of the data, this should provide a reliable method for anomaly detection. The first question this thesis addresses is how VAEs can be used for anomaly detection and how they perform in certain practical cases. Regular VAEs essentially compress high-dimensional data based only on an information bottleneck, but by extending the VAE framework we can model certain desirable properties of the real world. A particular example is disentangling independent generative factors. The idea is that data can be described by various real-world factors that represent independent mechanisms, and that representations should model these factors in separate latent subspaces. However, there is
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