Markovian Gaussian Process Variational Autoencoders
This work addresses computational inefficiency in continuous-time models for practitioners dealing with high-dimensional time series, though it is incremental as it builds on existing GPVAE methods.
The authors tackled the high computational cost of Gaussian process variational autoencoders (GPVAEs) by introducing Markovian GPVAE (MGPVAE), which uses a discrete state space representation to enable linear-time training via Kalman filtering and smoothing, achieving favorable performance on high-dimensional temporal and spatiotemporal tasks with improved scalability.
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.