mlsanityData to 7 Oct 2026

Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series

arXiv 2301.11308 ↗First posted 26 Jan 2023cs.LG cs.AI stat.MLcited by 28

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Abstract (arXiv)

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 22 of its 48 references that are in the map. First posted on arXiv 26 Jan 2023.

Builds on

22 of 48 references.

References · 22

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  3. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  4. 2020HiPPO: Recurrent Memory with Optimal Polynomial Projectionscited by 600
  5. 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 548
  6. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  7. 2015A Recurrent Latent Variable Model for Sequential Datacited by 362
  8. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  9. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  10. 2016Structured Inference Networks for Nonlinear State Space Modelscited by 182
  11. 2015Deep Kalman Filterscited by 163
  12. 2016Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Datacited by 154
10 more
  1. 2017A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learningcited by 107
  2. 2021Modeling Irregular Time Series with Continuous Recurrent Unitscited by 101
  3. 2018Probabilistic Recurrent State-Space Modelscited by 64
  4. 2018Learning unknown ODE models with Gaussian processescited by 54
  5. 2020Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filteringcited by 33
  6. 2019Collapsed Amortized Variational Inference for Switching Nonlinear Dynamical Systemscited by 26
  7. 2021Deep Explicit Duration Switching Models for Time Seriescited by 17
  8. 2021Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equationcited by 14
  9. 2019Intermittent Demand Forecasting with Deep Renewal Processescited by 6
  10. 2020Learning Continuous-Time Dynamics by Stochastic Differential Networkscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 11; 2025: 9; 2026: 8.

28 papers.

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  1. 2024ContiFormer: Continuous-Time Transformer for Irregular Time Series Modelingcited by 61
  2. 2025Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baselinecited by 54
  3. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 35
  4. 2024Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Modelscited by 31
  5. 2024Universal Time-Series Representation Learning: A Surveycited by 28
  6. 2024Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecastingcited by 18
  7. 2024Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Seriescited by 9
  8. 2025LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputationcited by 8
  9. 2025ASTGI: Adaptive Spatio-Temporal Graph Interactions for Irregular Multivariate Time Series Forecastingcited by 7
  10. 2024Temporal Test-Time Adaptation with State-Space Modelscited by 6
  11. 2024Latent Space Energy-based Neural ODEscited by 4
  12. 2025Neural Predictive Control to Coordinate Discrete- and Continuous-Time Models for Time-Series Analysis with Control-Theoretical Improvementscited by 3
16 more
  1. 2025Technologies on Effectiveness and Efficiency: A Survey of State Spaces Modelscited by 2
  2. 2025Modeling Irregular Astronomical Time Series with Neural Stochastic Delay Differential Equationscited by 2
  3. 2025Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutionscited by 2
  4. 2026MILM: Large Language Models for Multimodal Irregular Time Series with Informative Samplingcited by 2
  5. 2024Preparing for Black Swans: The Antifragility Imperative for Machine Learningcited by 1
  6. 2025Stochastic Optimal Control for Continuous-Time fMRI Representation Learningcited by 1
  7. 2026Auto-Configured Networks for Multi-Scale Multi-Output Time-Series Forecastingcited by 1
  8. 2026Neural Stochastic Processes for Satellite Precipitation Refinementcited by 1
  9. 2024Analyzing the Impact of Climate Change With Major Emphasis on Pollution: A Comparative Study of ML and Statistical Models in Time Series Datacited by 0
  10. 2024Marginalization Consistent Probabilistic Forecasting of Irregular Time Series via Mixture of Separable flowscited by 0
  11. 2025Neural Stochastic Differential Equations on Compact State Spaces: Theory, Methods, and Application to Suicide Risk Modelingcited by 0
  12. 2026Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecastingcited by 0
  13. 2026Physically-Constrained Mamba-SDE for Remaining Useful Life Prediction under Irregular Observationscited by 0
  14. 2026Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systemscited by 0
  15. 2026Dynestyx: A Probabilistic Programming Library for Dynamical Systemscited by 0
  16. 2026Continuous-Time Machine Learning: A Unified Mathematical Perspectivecited by 0

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  1. 2023Effectively Modeling Time Series with Simple Discrete State Spaces
  2. 2026Correct then Forecast: Observer State-Space Models for Time Series Forecasting
  3. 2024Deep Learning-based Approaches for State Space Models: A Selective Review
  4. 2024Oscillatory State-Space Models
  5. 2021Self-Supervised Inference in State-Space Models
  6. 2026Truncated Neural Likelihood Estimation for Simulation-Based Inference in State-Space Models
  7. 2024Variational quantization for state space models
  8. 2022Deep Latent State Space Models for Time-Series Generation