Factorized Gaussian Process Variational Autoencoders

Abstract

Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational autoencoders alleviate this problem through the use of a latent Gaussian process, but lead to a cubic inference time complexity. We propose a more scalable extension of these models by leveraging the independence of the auxiliary features, which is present in many datasets. Our model factorizes the latent kernel across these features in different dimensions, leading to a significant speed-up (in theory and practice), while empirically performing comparably to existing non-scalable approaches. Moreover, our approach allows for additional modeling of global latent information and for more general extrapolation to unseen input combinations. * Equal contribution.

Priors in Bayesian Deep Learning: A Review

“…However, this operation can be made more scalable, either through the use of inducing point methods (Ashman et al, 2020;Jazbec et al, 2021) (cf. Section 2.2) or through factorised kernels (Jazbec et al, 2020). Moreover, depending on the prior knowledge of the generative process, these models can also be extended to use additive GP priors (Ramchandran et al, 2020) or tensor-valued ones (Campbell & Liò, 2020).…”

Priors in Bayesian Deep Learning: A Review

“…( 6)). However, this operation can be made more scalable, either through the use of inducing point methods [116,117] (c.f., Section 2.2) or through factorized kernels [118]. Moreover, depending on the prior knowledge of the generative process, these models can also be extended to use additive GP priors [119] or tensor-valued ones [120].…”