Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, one can hope to detect out-of-distribution (abnormal) latent vectors, but several issues arise when the latent space is high dimensional. This includes an exponential growth of the hypervolume with the dimension, which severely affects the generative capacity of the VAE. In this paper, we draw insights from high dimensional statistics: in these regimes, the latent vectors of a standard VAE are distributed on the `equators' of a hypersphere, challenging the detection of anomalies. We propose to formulate the latent variables of a VAE using hyperspherical coordinates, which allows compressing the latent vectors towards a given direction on the hypersphere, thereby allowing for a more expressive approximate posterior. We show that this improves both the fully unconditional-OOD and conditional-OOD anomaly detection ability of the VAE, achieving the best performance on the datasets we considered, outperforming existing methods. For the unconditional-OOD and conditional-OOD modalities, respectively, these are: i) detecting unusual landscape from the Mars Rover camera and unusual Galaxies from ground based imagery (complex, real world datasets); ii) standard benchmarks like Cifar10 and subsets of ImageNet as the in-distribution (ID) class.

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