# Sampling-Free Probabilistic Deep State-Space Models

arXiv: https://arxiv.org/abs/2309.08256 · HTML: https://mlsanity.com/paper/2309.08256/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networks](https://mlsanity.com/paper/1605.07127/) (2016)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [Black box variational inference for state space models](https://mlsanity.com/paper/1511.07367/) (2015)
- [Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models](https://mlsanity.com/paper/1906.05828/) (2019)
- [Latent Neural ODEs with Sparse Bayesian Multiple Shooting](https://mlsanity.com/paper/2210.03466/) (2022)
- [Learning Partially Known Stochastic Dynamics with Empirical PAC Bayes](https://mlsanity.com/paper/2006.09914/) (2020)
- [Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Models](https://mlsanity.com/paper/2101.07046/) (2021)
- [Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equation](https://mlsanity.com/paper/2110.15739/) (2021)
- [Beyond the Mean-Field: Structured Deep Gaussian Processes Improve the Predictive Uncertainties](https://mlsanity.com/paper/2005.11110/) (2020)
- [A Deterministic Approximation to Neural SDEs](https://mlsanity.com/paper/2006.08973/) (2020)
- [Cheap and Deterministic Inference for Deep State-Space Models of Interacting Dynamical Systems](https://mlsanity.com/paper/2305.01773/) (2023)

## Built on by (most cited first, 2 of 2)

- [Exact nonlinear state estimation](https://mlsanity.com/paper/2310.10976/) (2023)
- [Motion Forecasting via Model-Based Risk Minimization](https://mlsanity.com/paper/2409.10585/) (2024)

## Abstract (arXiv)

Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM) generalizes this framework to dynamical systems of unknown parametric form, where the transition and emission models are described by neural networks with uncertain weights. In this work, we propose the first deterministic inference algorithm for models of this type. Our framework allows efficient approximations for training and testing. We demonstrate in our experiments that our new method can be employed for a variety of tasks and enjoys a superior balance between predictive performance and computational budget.