Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC

By Roger Frigola, Fredrik Lindsten, Thomas Bo Schön, Carl E. Rasmussen. 2013

167 citations recorded by the source corpus.

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

Subfields: Artificial Intelligence, Control and Systems Engineering, Signal Processing

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Citations in the corpus

Probabilistic Recurrent State-Space Models (2018, background): “Currently, no published and runnable code exists for the model learning frameworks presented in (Turner et al., 2010; Frigola et al., 2013; 2014; Eleftheriadis et al., 2017).”
Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks (2017, methodology): “ions such as VARs and SVRs. GP can be applied to multivariate time series forecasting task as suggested in [28], and can be used as a prior over the function space in Bayesian inference. For example, [10] presented a fully Bayesian approach with the GP prior for nonlinear state-space models, which i”
Applied Stochastic Differential Equations (2019, unknown): “Some iterated sigma-point smoothers have also been introduced by García-Fernández et al. (2017) and Tronarp et al. (2018), which in turn are based on the Gauss–Newton method interpretation of extended Kalman smoothers discussed in Bell (1994).”
FedLoc: Federated Learning Framework for Data-Driven Cooperative Localization and Location Data Processing (2020, methodology): “The ﬁrst fully probabilistic learning procedure of GPSSM was proposed in [126] using particle Markov Chain Monte Carlo (PMCMC).”
Particle gibbs with ancestor sampling (2014, methodology): “An example is the Gaussian process SSM (Turner and Deisenroth, 2010; Frigola et al., 2013), a flexible nonlinear dynamical systems model, for which PGAS has been successfully applied (Frigola et al., 2013).”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, background): “However, this model suffers from intractable inference since we need to marginalize out all the latent variables, thus requiring approximate inference [221], [226], [227].”