Nonlinear time-series prediction with missing and noisy data
Neural Computation
Physica D
The Handbook of Brain Theory and Neural Networks
The Handbook of Brain Theory and Neural Networks
Some Solutions to the Missing Feature Problem in Vision
Advances in Neural Information Processing Systems 5, [NIPS Conference]
Bayesian learning for neural networks
Bayesian learning for neural networks
Evaluation of gaussian processes and other methods for non-linear regression
Evaluation of gaussian processes and other methods for non-linear regression
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Nonlinear predictive control with a gaussian process model
Switching and Learning in Feedback Systems
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With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the covariance function of the process, we can evaluate these moments exactly or approximately (within a Taylor approximation of the covariance function). We apply our results to the iterative multiple-step ahead prediction of non-linear dynamic systems with propagation of the uncertainty as we predict ahead in time. Finally, using numerical examples, we compare the Gaussian approximation to the numerical approximation of the true predictive distribution by simple Monte-Carlo.