Scalable Gaussian Process Variational Autoencoders

Variational autoencoders (VAEs) are among the most widely used models in representation learning and generative modeling (Kingma and Welling, 2013, 2019; Rezende et al., 2014). As VAEs typically make use of factorized priors, they fall short when modeling correlations between different data points. However, more expressive priors that capture correlations enable useful applications. Casale et al. (2018), for instance, showed that by modeling prior correlations between the data, one could generate a digit's rotated image based on rotations of the same digit at different angles. Gaussian process VAEs (GP-VAEs) have been designed to overcome this shortcoming (Casale et al., 2018). These models introduce a Gaussian process (GP) prior over the latent variables that correlates pairs of latent variables through a kernel function. While GP-VAEs have outperformed standard VAEs on many tasks (Casale et al., 2018; Fortuin et al., 2020; Pearce, 2020), combining the GPs and VAEs brings along fundamental computational challenges. On the one hand, neural networks reveal their full power in conjunction with large datasets, making mini-batching a practical necessity. GPs, on the other hand, are traditionally restricted to medium-scale datasets due to their unfavorable scaling.