Identification of Gaussian Process State Space Models

2017/05/30 by Stefanos Eleftheriadis, Eleftheriadis, Stefanos, Thomas F. W. Nicholson +5 · 2 citations
Computer Science · Engineering · #Control Systems and Identification #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.1705.10888

openalex publication_date 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior of the latent state given the model. However, the key challenge in GPSSMs has not been satisfactorily addressed yet: system identification, i.e., learning the model. To address this challenge, we impose a structured Gaussian variational posterior distribution over the latent states, which is parameterised by a recognition model in the form of a bi-directional recurrent neural network. Inference with this structure allows us to recover a posterior smoothed over sequences of data. We provide a practical algorithm for efficiently computing a lower bound on the marginal likelihood using the reparameterisation trick. This further allows for the use of arbitrary kernels within the GPSSM. We demonstrate that the learnt GPSSM can efficiently generate plausible future trajectories of the identified system after only observing a small number of episodes from the true system.

Citations

• Auto-Encoding Variational Bayes
• On the Properties of Neural Machine Translation: Encoder-Decoder Approaches

Cited by

• Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches
• Gaussian Process State-Space Modeling and Particle Filtering for Time Series Decomposition and Nonlinear Signal Extraction

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