mlsanityData to 7 Oct 2026

Markovian Gaussian Process Variational Autoencoders

arXiv 2207.05543 ↗First posted 12 Jul 2022cs.LG cs.CV stat.MLcited by 16

Not on the map. Why?

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.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 38 of its 73 references that are in the map. First posted on arXiv 12 Jul 2022.

Builds on

38 of 73 references.

References · 38

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  3. 2014On the Properties of Neural Machine Translation: Encoder-Decoder Approachescited by 1,303
  4. 2013Gaussian Processes for Big Datacited by 377
  5. 2020dm_control: Software and Tasks for Continuous Controlcited by 368
  6. 2015A Recurrent Latent Variable Model for Sequential Datacited by 362
  7. 2013Black Box Variational Inferencecited by 317
  8. 2021Skillful Precipitation Nowcasting using Deep Generative Models of Radarcited by 308
  9. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  10. 2022On Neural Differential Equationscited by 264
  11. 2014Scalable Variational Gaussian Process Classificationcited by 226
  12. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 188
26 more
  1. 2016Variational Lossy Autoencodercited by 175
  2. 2019GP-VAE: Deep Probabilistic Time Series Imputationcited by 171
  3. 2022It's Raw! Audio Generation with State-Space Modelscited by 171
  4. 2018Handling Incomplete Heterogeneous Data using VAEscited by 148
  5. 2019Neural Jump Stochastic Differential Equationscited by 147
  6. 2016GPflow: A Gaussian process library using TensorFlowcited by 139
  7. 2013Gaussian Process Kernels for Pattern Discovery and Extrapolationcited by 131
  8. 2018Disentangled Sequential Autoencodercited by 117
  9. 2017A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learningcited by 107
  10. 2021Modeling Irregular Time Series with Continuous Recurrent Unitscited by 101
  11. 2018Gaussian Process Prior Variational Autoencoderscited by 72
  12. 2017Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Modelscited by 65
  13. 2019Rates of Convergence for Sparse Variational Gaussian Process Regressioncited by 62
  14. 2017Dynamic Word Embeddingscited by 51
  15. 2020Vid-ODE: Continuous-Time Video Generation with Neural Ordinary Differential Equationcited by 39
  16. 2021Spatio-Temporal Variational Gaussian Processescited by 32
  17. 2019Temporal Parallelization of Bayesian Smootherscited by 31
  18. 2020Sparse Gaussian Process Variational Autoencoderscited by 21
  19. 2020Fast Variational Learning in State-Space Gaussian Process Modelscited by 20
  20. 2020Scalable Gaussian Process Variational Autoencoderscited by 20
  21. 2020Doubly Sparse Variational Gaussian Processescited by 14
  22. 2021Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guaranteescited by 12
  23. 2020State Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processescited by 10
  24. 2021Sparse Algorithms for Markovian Gaussian Processescited by 10
  25. 2021Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processescited by 7
  26. 2022Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classificationcited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 6; 2025: 5; 2026: 1.

16 papers.

Sort:

By area:

  1. 2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 48
  2. 2023Fully Bayesian Autoencoders with Latent Sparse Gaussian Processescited by 9
  3. 2024Temporal Test-Time Adaptation with State-Space Modelscited by 6
  4. 2024Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regionscited by 5
  5. 2022Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilationcited by 4
  6. 2024Preventing Model Collapse in Gaussian Process Latent Variable Modelscited by 3
  7. 2024Latent mixed-effect models for high-dimensional longitudinal datacited by 3
  8. 2025Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modellingcited by 3
  9. 2024Weakly Augmented Variational Autoencoder in Time Series Anomaly Detectioncited by 2
  10. 2025Recurrent Memory for Online Interdomain Gaussian Processescited by 2
  11. 2026AR-Flow VAE: A Structured Autoregressive Flow Prior Variational Autoencoder for Unsupervised Blind Source Separationcited by 2
  12. 2023Deep Latent Force Models: ODE-based Process Convolutions for Bayesian Deep Learningcited by 1
4 more
  1. 2025Temporal Cardiovascular Dynamics for Improved PPG-Based Heart Rate Estimationcited by 1
  2. 2024Diffusion Model from Scratchcited by 0
  3. 2025Likelihood-Free Variational Autoencoderscited by 0
  4. 2025PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoderscited by 0