mlsanityData to 7 Oct 2026

Deep Stochastic Processes via Functional Markov Transition Operators

arXiv 2305.15574 ↗First posted 24 May 2023stat.ML cs.LGcited by 7

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Abstract (arXiv)

We introduce Markov Neural Processes (MNPs), a new class of Stochastic Processes (SPs) which are constructed by stacking sequences of neural parameterised Markov transition operators in function space. We prove that these Markov transition operators can preserve the exchangeability and consistency of SPs. Therefore, the proposed iterative construction adds substantial flexibility and expressivity to the original framework of Neural Processes (NPs) without compromising consistency or adding restrictions. Our experiments demonstrate clear advantages of MNPs over baseline models on a variety of tasks.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 30 of its 57 references that are in the map. First posted on arXiv 24 May 2023.

Builds on

30 of 57 references.

References · 30

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  5. 2015Variational Inference with Normalizing Flowscited by 2,161
  6. 2017Deep Setscited by 1,394
  7. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  8. 2018A Tutorial on Bayesian Optimizationcited by 734
  9. 2019Neural Spline Flowscited by 590
  10. 2015Importance Weighted Autoencoderscited by 454
  11. 2018Conditional Neural Processescited by 421
  12. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 281
18 more
  1. 2019Attentive Neural Processescited by 280
  2. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  3. 2018Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Samplingcited by 166
  4. 2019Convolutional Conditional Neural Processescited by 139
  5. 2023Modern Bayesian Experimental Designcited by 121
  6. 2021Generative Models as Distributions of Functionscited by 89
  7. 2020Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processescited by 74
  8. 2023Prediction-Oriented Bayesian Active Learningcited by 60
  9. 2022Neural Diffusion Processescited by 50
  10. 2014Student-t Processes as Alternatives to Gaussian Processescited by 45
  11. 2019MetaFun: Meta-Learning with Iterative Functional Updatescited by 34
  12. 2021The Gaussian Neural Processcited by 34
  13. 2020Transforming Gaussian Processes With Normalizing Flowscited by 28
  14. 2018Parametric generation of conditional geological realizations using generative neural networkscited by 19
  15. 2021Group Equivariant Conditional Neural Processescited by 16
  16. 2018Generating Realistic Geology Conditioned on Physical Measurements with Generative Adversarial Networkscited by 12
  17. 2021On Contrastive Representations of Stochastic Processescited by 12
  18. 2018BRUNO: A Deep Recurrent Model for Exchangeable Datacited by 11

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 3; 2026: 2.

7 papers.

  1. 2025Flow Matching Neural Processescited by 6
  2. 2023Learning multi-modal generative models with permutation-invariant encoders and tighter variational objectivescited by 4
  3. 2024Spectral Convolutional Conditional Neural Processescited by 4
  4. 2025Exploring Pseudo-Token Approaches in Transformer Neural Processescited by 2
  5. 2026Incremental Transformer Neural Processescited by 2
  6. 2025Continual learning via probabilistic exchangeable sequence modellingcited by 0
  7. 2026Revisiting Neural Processes via Fourier Transform and Volterra Seriescited by 0