Gaussian process regression with multiple response variables

By Bo Wang, Tao Chen. 2015

117 citations recorded by the source corpus.

Abstract Gaussian process regression (GPR) is a Bayesian non-parametric technology that has gained extensive application in data-based modelling of various systems, including those of interest to chemometrics. However, most GPR implementations model only a single response variable, due to the difficulty in the formulation of covariance function for correlated multiple response variables, which describes not only the correlation between data points, but also the correlation between responses. In the paper we propose a direct formulation of the covariance function for multi-response GPR, based on the idea that its covariance function is assumed to be the “nominal” uni-output covariance multiplied by the covariances between different outputs. The effectiveness of the proposed multi-response GPR method is illustrated through numerical examples and response surface modelling of a catalytic reaction process.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0b0b3191d3da736cd745fbabe6204de0b640a1f0

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Citations in the corpus

Groundwater level prediction in arid areas using wavelet analysis and Gaussian process regression (2021, background): “…of maximum likelihood computation (Wang & Chen, 2015): L = ( −1 2 ) log(detC)− 1 2 yTC−1y − n 2 log(2π) (9) Equation (10) presents the derivative of the loglikelihood with respect to each hyper parameter (Wang & Chen, 2015): ∂L ∂θ = ( −1 2 ) tr ( C−1 ∂C ∂θ ) + ( 1 2 ) yTC−1 ( ∂C ∂θ ) C−1y (10)”
Online Sparse Multi-Output Gaussian Process Regression and Learning (2019, methodology): “First, we consider simultaneously modeling the following two well-correlated bivariate functions [19]”