42 Anomaly Detection with Variational Autoencoders To exemplify this, we look at two cases specifically, where the anomalies are the digits 0 and 7, respectively. Density plots for both of these cases, for the 2 and 32-dimensional models, are shown in Figure 3.9. We observe better separation of ELBO values for the 2-dimensional model. For anomalous digit 7 we notice in particular that the 32-dimensional model yields an almost complete overlap in ELBO score distribution between normal images and anomalies. (a) Anomalous digit 0. Latent dimension 2. (b) Anomalous digit 7. Latent dimension 2. (c) Anomalous digit 0. Latent dimension 32. (d) Anomalous digit 7. Latent dimension 32. Figure 3.9: ELBO density distributions for normal (blue) and anomalous (red) MNIST digits. We can better understand how this happens by taking some examples and looking at their VAE reconstructions. Figure 3.10 shows anomalous images and their reconstructions, as well as a visualisation of the difference between the two. We observe that the 2-dimensional model reconstructs anomalous digits into images representing “normal” digits instead, whereas the 32-dimensional
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