Gaussian process

About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.

Kalman filtering and smoothing solutions to temporal Gaussian process regression models

Abstract: In this paper, we show how temporal (i.e., time-series) Gaussian process regression models in machine learning can be reformulated as linear-Gaussian state space models, which can be solved exactly with classical Kalman filtering theory. The result is an efficient non-parametric learning algorithm, whose computational complexity grows linearly with respect to number of observations. We show how the reformulation can be done for Matern family of covariance functions analytically and for squared exponential covariance function by applying spectral Taylor series approximation. Advantages of the proposed approach are illustrated with two numerical experiments.

Semiparametric Latent Factor Models

Abstract: We propose a semiparametric model for regression and classification problems involving multiple response variables. The model makes use of a set of Gaussian processes to model the relationship to the inputs in a nonparametric fashion. Conditional dependencies between the responses can be captured through a linear mixture of the driving processes. This feature becomes important if some of the responses of predictive interest are less densely supplied by observed data than related auxiliary ones. We propose an efficient approximate inference scheme for this semiparametric model whose complexity is linear in the number of training data points.

The Distribution of Products of Beta, Gamma and Gaussian Random Variables

Abstract: The probability density functions of products of independent beta, gamma and central Gaussian random variables are shown to be Meijer G-functions. The density function of products of random beta va...

Variational Heteroscedastic Gaussian Process Regression

Abstract: Standard Gaussian processes (GPs) model observations' noise as constant throughout input space. This is often a too restrictive assumption, but one that is needed for GP inference to be tractable. In this work we present a non-standard variational approximation that allows accurate inference in heteroscedastic GPs (i.e., under input-dependent noise conditions). Computational cost is roughly twice that of the standard GP, and also scales as O(n3). Accuracy is verified by comparing with the golden standard MCMC and its effectiveness is illustrated on several synthetic and real datasets of diverse characteristics. An application to volatility forecasting is also considered.