# Markovian Gaussian Process Variational Autoencoders

arXiv: https://arxiv.org/abs/2207.05543 · HTML: https://mlsanity.com/paper/2207.05543/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 73 references that are in the map.
- First posted on arXiv 12 Jul 2022.

## Builds on (most cited first, 30 of 38)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models](https://mlsanity.com/paper/1703.04265/) (2017)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Dynamic Word Embeddings](https://mlsanity.com/paper/1702.08359/) (2017)
- [Vid-ODE: Continuous-Time Video Generation with Neural Ordinary Differential Equation](https://mlsanity.com/paper/2010.08188/) (2020)
- [Temporal Parallelization of Bayesian Smoothers](https://mlsanity.com/paper/1905.13002/) (2019)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Sparse Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2010.10177/) (2020)

## Built on by (most cited first, 16 of 16)

- [Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs](https://mlsanity.com/paper/2310.02619/) (2023)
- [Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes](https://mlsanity.com/paper/2302.04534/) (2023)
- [Temporal Test-Time Adaptation with State-Space Models](https://mlsanity.com/paper/2407.12492/) (2024)
- [Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation](https://mlsanity.com/paper/2209.15609/) (2022)
- [Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions](https://mlsanity.com/paper/2402.02686/) (2024)
- [Preventing Model Collapse in Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2404.01697/) (2024)
- [Latent mixed-effect models for high-dimensional longitudinal data](https://mlsanity.com/paper/2409.11008/) (2024)
- [Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modelling](https://mlsanity.com/paper/2505.16481/) (2025)
- [Weakly Augmented Variational Autoencoder in Time Series Anomaly Detection](https://mlsanity.com/paper/2401.03341/) (2024)
- [Recurrent Memory for Online Interdomain Gaussian Processes](https://mlsanity.com/paper/2502.08736/) (2025)
- [AR-Flow VAE: A Structured Autoregressive Flow Prior Variational Autoencoder for Unsupervised Blind Source Separation](https://mlsanity.com/paper/2603.14441/) (2026)
- [Deep Latent Force Models: ODE-based Process Convolutions for Bayesian Deep Learning](https://mlsanity.com/paper/2311.14828/) (2023)
- [Temporal Cardiovascular Dynamics for Improved PPG-Based Heart Rate Estimation](https://mlsanity.com/paper/2510.27297/) (2025)
- [Diffusion Model from Scratch](https://mlsanity.com/paper/2412.10824/) (2024)
- [Likelihood-Free Variational Autoencoders](https://mlsanity.com/paper/2504.17622/) (2025)
- [PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2505.19320/) (2025)

## Abstract (arXiv)

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.