mlsanityData to 7 Oct 2026

Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting

arXiv 2102.00397 ↗First posted 31 Jan 2021cs.LG stat.MLcited by 29

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Abstract (arXiv)

Probabilistic time series forecasting involves estimating the distribution of future based on its history, which is essential for risk management in downstream decision-making. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks and the dependency is modeled by recurrent neural nets. We take the automatic relevance determination (ARD) view and devise a network to exploit the exogenous variables in addition to time series. In particular, our ARD network can incorporate the uncertainty of the exogenous variables and eventually helps identify useful exogenous variables and suppress those irrelevant for forecasting. The distribution of multi-step ahead forecasts are approximated by Monte Carlo simulation. We show in experiments that our model produces accurate and sharp probabilistic forecasts. The estimated uncertainty of our forecasting also realistically increases over time, in a spontaneous manner.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Builds on 13 of its 35 references that are in the map. First posted on arXiv 31 Jan 2021.

Builds on

13 of 35 references.

References · 13

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  3. 2013Auto-Encoding Variational Bayescited by 3,980
  4. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  5. 2015Importance Weighted Autoencoderscited by 454
  6. 2015A Recurrent Latent Variable Model for Sequential Datacited by 362
  7. 2017A Multi-Horizon Quantile Recurrent Forecastercited by 211
  8. 2016Structured Inference Networks for Nonlinear State Space Modelscited by 182
  9. 2015Deep Kalman Filterscited by 163
  10. 2016Sequential Neural Models with Stochastic Layerscited by 115
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  12. 2017Identification of Gaussian Process State Space Modelscited by 31
1 more
  1. 2013Variational Relevance Vector Machinescited by 21

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 9; 2023: 7; 2024: 3; 2025: 3; 2026: 3.

29 papers.

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  1. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
  2. 2023Large Pre-trained time series models for cross-domain Time series analysis taskscited by 22
  3. 2022Multi-scale Attention Flow for Probabilistic Time Series Forecastingcited by 19
  4. 2021CAMul: Calibrated and Accurate Multi-view Time-Series Forecastingcited by 17
  5. 2021RNN with Particle Flow for Probabilistic Spatio-temporal Forecastingcited by 16
  6. 2023Traffic Prediction using Artificial Intelligence: Review of Recent Advances and Emerging Opportunitiescited by 16
  7. 2021SSDNet: State Space Decomposition Neural Network for Time Series Forecastingcited by 15
  8. 2023A Systematic Review for Transformer-based Long-term Series Forecastingcited by 10
  9. 2023Hybrid Variational Autoencoder for Time Series Forecastingcited by 8
  10. 2025K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecastingcited by 7
  11. 2024A Gated Residual Kolmogorov-Arnold Networks for Mixtures of Expertscited by 6
  12. 2022When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecastingcited by 4
17 more
  1. 2024A Temporal Linear Network for Time Series Forecastingcited by 4
  2. 2025Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamicscited by 4
  3. 2022AA-Forecast: Anomaly-Aware Forecast for Extreme Eventscited by 3
  4. 2023PEMS: Pre-trained Epidemic Time-series Modelscited by 3
  5. 2024HiPPO-KAN: Efficient KAN Model for Time Series Analysiscited by 3
  6. 2021Deep Probabilistic Time Series Forecasting using Augmented Recurrent Input for Dynamic Systemscited by 1
  7. 2022Recurrence Boosts Diversity! Revisiting Recurrent Latent Variable in Transformer-Based Variational AutoEncoder for Diverse Text Generationcited by 1
  8. 2023DANLIP: Deep Autoregressive Networks for Locally Interpretable Probabilistic Forecastingcited by 1
  9. 2022Interpretable Latent Variables in Deep State Space Modelscited by 0
  10. 2022Monitoring Time Series With Missing Values: a Deep Probabilistic Approachcited by 0
  11. 2022Why Did This Model Forecast This Future? Closed-Form Temporal Saliency Towards Causal Explanations of Probabilistic Forecastscited by 0
  12. 2022Neural State-Space Modeling with Latent Causal-Effect Disentanglementcited by 0
  13. 2023When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecastingcited by 0
  14. 2025STAN: Smooth Transition Autoregressive Networkscited by 0
  15. 2026Efficient Learning of Deep State Space Models via Importance Smoothingcited by 0
  16. 2026ProbRes: Volatility Learning for Probabilistic Time-Series Forecastingcited by 0
  17. 2026XMatch: Enhancing Covariate-Aware Time Series Forecasting through Tree-Structured Exogenous Matchingcited by 0

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  1. 2021Stochastic Recurrent Neural Network for Multistep Time Series Forecasting
  2. 2026DeRegiME: Deep Regime Mixtures for Probabilistic Forecasting under Distribution Shift
  3. 2024SDE: A Simplified and Disentangled Dependency Encoding Framework for State Space Models in Time Series Forecasting
  4. 2023Effectively Modeling Time Series with Simple Discrete State Spaces
  5. 2026Rethinking Recurrent Neural Networks for Time Series Forecasting: A Reinforced Recurrent Encoder with Prediction-Oriented Proximal Policy Optimization
  6. 2024A Comprehensive Survey of Deep Learning for Time Series Forecasting: Architectural Diversity and Open Challenges
  7. 2026A Decomposition-based State Space Model for Multivariate Time-Series Forecasting
  8. 2025LLM-Integrated Bayesian State Space Models for Multimodal Time-Series Forecasting