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

• URL: http://arxiv.org/abs/2006.04788v1
• Date: Mon, 8 Jun 2020 17:59:13 GMT
• Title: tvGP-VAE: Tensor-variate Gaussian Process Prior Variational Autoencoder
• Authors: Alex Campbell, Pietro Li\`o
• Abstract summary: tvGP-VAE is able to explicitly model correlation via the use of kernel functions. We show that the choice of which correlation structures to explicitly represent in the latent space has a significant impact on model performance.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational autoencoders (VAEs) are a powerful class of deep generative latent variable model for unsupervised representation learning on high-dimensional data. To ensure computational tractability, VAEs are often implemented with a univariate standard Gaussian prior and a mean-field Gaussian variational posterior distribution. This results in a vector-valued latent variables that are agnostic to the original data structure which might be highly correlated across and within multiple dimensions. We propose a tensor-variate extension to the VAE framework, the tensor-variate Gaussian process prior variational autoencoder (tvGP-VAE), which replaces the standard univariate Gaussian prior and posterior distributions with tensor-variate Gaussian processes. The tvGP-VAE is able to explicitly model correlation structures via the use of kernel functions over the dimensions of tensor-valued latent variables. Using spatiotemporally correlated image time series as an example, we show that the choice of which correlation structures to explicitly represent in the latent space has a significant impact on model performance in terms of reconstruction.

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