Data to 7 Oct 2026

Structured Inference Networks for Nonlinear State Space Models

arXiv 1609.09869 ↗First posted 30 Sep 2016stat.ML cs.AI cs.LGcited by 182

Not on the map. Why?

Abstract (arXiv)

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.

Key facts. Cited by 182 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Sep 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 46; 2022: 33; 2023: 32; 2024: 25; 2025: 17; 2026: 29.

182 papers.

Sort:

By area:

2024Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusioncited by 634
2024Deep Time Series Models: A Comprehensive Survey and Benchmarkcited by 191
2021KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamicscited by 128
2022Unsupervised Time-Series Representation Learning with Iterative Bilinear Temporal-Spectral Fusioncited by 96
2021Proximal Optimal Transport Modeling of Population Dynamicscited by 91
2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
2021Differentiable Particle Filtering via Entropy-Regularized Optimal Transportcited by 59
2021Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modelingcited by 59
2023TimesURL: Self-supervised Contrastive Learning for Universal Time Series Representation Learningcited by 51
2022Criteria for Classifying Forecasting Methodscited by 48
2022StretchBEV: Stretching Future Instance Prediction Spatially and Temporallycited by 47
2022Contrastive Learning for Unsupervised Domain Adaptation of Time Seriescited by 36

38 more

2022Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systemscited by 34
2021Time Series Anomaly Detection for Cyber-Physical Systems via Neural System Identification and Bayesian Filteringcited by 31
2021Dynamic Gaussian Mixture based Deep Generative Model For Robust Forecasting on Sparse Multivariate Time Seriescited by 30
2021Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecastingcited by 29
2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
2021Unsupervised Speech Enhancement using Dynamical Variational Auto-Encoderscited by 28
2021Auto-differentiable Ensemble Kalman Filterscited by 28
2023Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Seriescited by 28
2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
2023Large Pre-trained time series models for cross-domain Time series analysis taskscited by 22
2021Online Variational Filtering and Parameter Learningcited by 19
2022Multi-scale Attention Flow for Probabilistic Time Series Forecastingcited by 19
2023DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setupcited by 19
2021CAMul: Calibrated and Accurate Multi-view Time-Series Forecastingcited by 17
2021Unsupervised Learned Kalman Filteringcited by 17
2024RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomaliescited by 17
2021ACE-NODE: Attentive Co-Evolving Neural Ordinary Differential Equationscited by 15
2021Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Modelscited by 14
2021AttDMM: An Attentive Deep Markov Model for Risk Scoring in Intensive Care Unitscited by 14
2022Neural Ordinary Differential Equations for Nonlinear System Identificationcited by 14
2022On Uncertainty in Deep State Space Models for Model-Based Reinforcement Learningcited by 13
2021Neural Pharmacodynamic State Space Modelingcited by 12
2021HYPER: Learned Hybrid Trajectory Prediction via Factored Inference and Adaptive Samplingcited by 12
2021The Medkit-Learn(ing) Environment: Medical Decision Modelling through Simulationcited by 11
2021Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertaintycited by 11
2021A Hierarchical Variational Neural Uncertainty Model for Stochastic Video Predictioncited by 10
2021Dynamical Wasserstein Barycenters for Time-series Modelingcited by 10
2021Constrained Block Nonlinear Neural Dynamical Modelscited by 9
2024KalMamba: Towards Efficient Probabilistic State Space Models for RL under Uncertaintycited by 9
2022Low-Rank Constraints for Fast Inference in Structured Modelscited by 8
2022Hidden Parameter Recurrent State Space Models For Changing Dynamics Scenarioscited by 8
2022Neural Extended Kalman Filters for Learning and Predicting Dynamics of Structural Systemscited by 8
2023Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networkscited by 8
2025Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Modelscited by 8
2021Deformable Linear Object Prediction Using Locally Linear Latent Dynamicscited by 7
2022GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductionscited by 7
2023Multi Time Scale World Modelscited by 7
2024eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modelingcited by 7

50 most cited of 182 All 182 (JSON)