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

arXiv: https://arxiv.org/abs/2006.04788 · HTML: https://mlsanity.com/paper/2006.04788/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Physics-enhanced Gaussian Process Variational Autoencoder](https://mlsanity.com/paper/2305.09006/) (2023)
- [Structured Recognition for Generative Models with Explaining Away](https://mlsanity.com/paper/2209.05212/) (2022)
- [Stability Enhanced Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2604.09331/) (2026)

## Abstract (arXiv)

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.