# Recursive Gaussian Process State Space Model

arXiv: https://arxiv.org/abs/2411.14679 · HTML: https://mlsanity.com/paper/2411.14679/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 89 references that are in the map.
- First posted on arXiv 22 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [Deep State Space Models for Nonlinear System Identification](https://mlsanity.com/paper/2003.14162/) (2020)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models](https://mlsanity.com/paper/1906.05828/) (2019)
- [A flexible state space model for learning nonlinear dynamical systems](https://mlsanity.com/paper/1603.05486/) (2016)
- [Incremental Ensemble Gaussian Processes](https://mlsanity.com/paper/2110.06777/) (2021)
- [Streaming Variational Monte Carlo](https://mlsanity.com/paper/1906.01549/) (2019)
- [Gaussian Process Volatility Model](https://mlsanity.com/paper/1402.3085/) (2014)
- [Free-Form Variational Inference for Gaussian Process State-Space Models](https://mlsanity.com/paper/2302.09921/) (2023)
- [eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling](https://mlsanity.com/paper/2403.01371/) (2024)
- [Sequential Estimation of Gaussian Process-based Deep State-Space Models](https://mlsanity.com/paper/2301.12528/) (2023)
- [Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference](https://mlsanity.com/paper/2312.05910/) (2023)
- [Data-driven predictive control in a stochastic setting: a unified framework](https://mlsanity.com/paper/2203.10846/) (2022)
- [System Identification through Online Sparse Gaussian Process Regression with Input Noise](https://mlsanity.com/paper/1601.08068/) (2016)
- [Online Gaussian Process State-Space Model: Learning and Planning for Partially Observable Dynamical Systems](https://mlsanity.com/paper/1903.08643/) (2019)
- [Learning Driver Behaviors Using A Gaussian Process Augmented State-Space Model](https://mlsanity.com/paper/2003.07312/) (2020)
- [A Novel Vector-Field-Based Motion Planning Algorithm for 3D Nonholonomic Robots](https://mlsanity.com/paper/2302.11110/) (2023)
- [Dynamically Iterated Filters: A unified framework for improved iterated filtering and smoothing](https://mlsanity.com/paper/2404.15359/) (2024)

## Abstract (arXiv)

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models (GPSSMs) have recently gained significant attention due to their combination of flexibility and interpretability. However, for online learning, the field lacks an efficient method suitable for scenarios where prior information regarding data distribution and model function is limited. To address this issue, this paper proposes a recursive GPSSM method with adaptive capabilities for both operating domains and Gaussian process (GP) hyperparameters. Specifically, we first utilize first-order linearization to derive a Bayesian update equation for the joint distribution between the system state and the GP model, enabling closed-form and domain-independent learning. Second, an online selection algorithm for inducing points is developed based on informative criteria to achieve lightweight learning. Third, to support online hyperparameter optimization, we recover historical measurement information from the current filtering distribution. Comprehensive evaluations on both synthetic and real-world datasets demonstrate the superior accuracy, computational efficiency, and adaptability of our method compared to state-of-the-art online GPSSM techniques.