Markovian Gaussian Process Variational Autoencoders

TL;DR

This paper introduces Markovian GPVAE, a scalable continuous-time VAE model for high-dimensional time series that leverages Markovian GPs for linear-time training, outperforming existing methods in accuracy and efficiency.

Contribution

We propose Markovian GPVAE, a novel continuous-time VAE that uses Markovian Gaussian processes for linear-time training, addressing computational limitations of traditional GPVAEs.

Findings

Performs favorably on high-dimensional temporal tasks.

Achieves linear training complexity via Kalman filtering.

Outperforms existing approaches in accuracy and scalability.

Abstract

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. For our model, Markovian GPVAE (MGPVAE), we show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.