• Corpus ID: 54462057

Closed-form Inference and Prediction in Gaussian Process State-Space Models

@article{Ialongo2018ClosedformIA,
  title={Closed-form Inference and Prediction in Gaussian Process State-Space Models},
  author={Alessandro Davide Ialongo and Mark van der Wilk and Carl Edward Rasmussen},
  journal={ArXiv},
  year={2018},
  volume={abs/1812.03580}
}
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the system states and the transition function. We exploit Markov structure in the true posterior, as well as an inducing point approximation to achieve linear time complexity in the length of the time series. Contrary to previous approaches, no Monte Carlo sampling… 
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References

SHOWING 1-6 OF 6 REFERENCES

Variational Gaussian Process State-Space Models

This work presents a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes and offers the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting.

Gaussian Process Priors with Uncertain Inputs - Application to Multiple-Step Ahead Time Series Forecasting

This paper shows how an analytical Gaussian approximation can formally incorporate the uncertainty about intermediate regressor values, thus updating the uncertainty on the current prediction of the multi-step ahead prediction in time series analysis.

On Sparse Variational Methods and the Kullback-Leibler Divergence between Stochastic Processes

A substantial generalization of the literature on variational framework for learning inducing variables is given and a new proof of the result for infinite index sets is given which allows inducing points that are not data points and likelihoods that depend on all function values.

PILCO: A Model-Based and Data-Efficient Approach to Policy Search

PILCO reduces model bias, one of the key problems of model-based reinforcement learning, in a principled way by learning a probabilistic dynamics model and explicitly incorporating model uncertainty into long-term planning.

Variational Learning of Inducing Variables in Sparse Gaussian Processes

A variational formulation for sparse approximations that jointly infers the inducing inputs and the kernel hyperparameters by maximizing a lower bound of the true log marginal likelihood.

Nonlinear modelling and control using Gaussian processes

  • PhD thesis, PhD thesis,
  • 2014