# Computationally Efficient Bayesian Learning of Gaussian Process State Space Models

@inproceedings{Svensson2016ComputationallyEB, title={Computationally Efficient Bayesian Learning of Gaussian Process State Space Models}, author={Andreas Svensson and A. Solin and Simo S{\"a}rkk{\"a} and Thomas Bo Sch{\"o}n}, booktitle={AISTATS}, year={2016} }

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure. Learning under this family of models can be conducted using a carefully crafted particle MCMC algorithm. This scheme is computationally… Expand

#### 41 Citations

Recursive Bayesian Inference and Learning of Gaussian-Process State-Space Models

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- 2019

The results indicate that the method efficiently learns the system jointly with estimating the state, and that the approach for certain scenarios gives similar performance as more computation-heavy offline approaches. Expand

Rao-Blackwellized particle mcmc for parameter estimation in spatio-temporal Gaussian processes

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In this paper, we consider parameter estimation in latent, spatiotemporal Gaussian processes using particle Markov chain Monte Carlo methods. In particular, we use spectral decomposition of the… Expand

Identification of Gaussian Process State Space Models

- Mathematics, Computer Science
- NIPS
- 2017

A structured Gaussian variational posterior distribution over the latent states is imposed, which is parameterised by a recognition model in the form of a bi-directional recurrent neural network, which allows for the use of arbitrary kernels within the GPSSM. Expand

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- Computer Science, Mathematics
- ArXiv
- 2018

This work presents the particle stochastic approximation EM (PSAEM) algorithm, an iterative procedure for maximum likelihood inference in latent variable models that obtains superior computational performance and convergence properties compared to plain particle-smoothing-based approximations of the EM algorithm. Expand

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- Computer Science, Mathematics
- 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
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This paper uses a basis function expansion within the state space model to obtain a flexible structure and proposes a regularization scheme without increasing the computational burden, which opens up for systematic use of regularization in nonlinear state space models. Expand

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- Mathematics, Computer Science
- Autom.
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A nonlinear state-space model with the state transition and observation functions expressed as basis function expansions is considered, using a connection to Gaussian processes to develop priors on the coefficients, for tuning the model flexibility and to prevent overfitting to data. Expand

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- ICML
- 2018

This work proposes to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism and demonstrates the model's capabilities to infer dynamics from sparse data and to simulate the system forward into future. Expand

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- 2015

A filtered nonlinear auto-regressive model with a simple, robust and fast learning algorithm that makes it well suited to its application by non-experts on large datasets, and avoids the computationally expensive smoothing step that is a key part of learning non-linear state-space models. Expand

The Use of Gaussian Processes in System Identification

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- 2019

In system identification, Gaussian processes are used to form time series prediction models such as non-linear finite-impulse response (NFIR) models as well asnon-linear autoregressive (NARX) models. Expand

The Use of Gaussian Processes in System Identification

- Mathematics, Computer Science
- ArXiv
- 2019

In system identification, Gaussian processes are used to form time series prediction models such as non-linear finite-impulse response (NFIR) models as well asnon-linear autoregressive (NARX) models. Expand

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