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Variational autoencoders (VAEs) are a powerful class of deep generativelatent variable model for unsupervised representation learning onhigh-dimensional data. To ensure computational tractability, VAEs are oftenimplemented with a univariate standard Gaussian prior and a mean-field Gaussianvariational posterior distribution. This results in a vector-valued latentvariables that are agnostic to the original data structure which might behighly correlated across and within multiple dimensions. We propose atensor-variate extension to the VAE framework, the tensor-variate Gaussianprocess prior variational autoencoder (tvGP-VAE), which replaces the standardunivariate Gaussian prior and posterior distributions with tensor-variateGaussian processes. The tvGP-VAE is able to explicitly model correlationstructures via the use of kernel functions over the dimensions of tensor-valuedlatent variables. Using spatiotemporally correlated image time series as anexample, we show that the choice of which correlation structures to explicitlyrepresent in the latent space has a significant impact on model performance interms of reconstruction.

tvGP-VAE: Tensor-variate Gaussian Process Prior Variational Autoencoder