Posterior contraction in Gaussian process regression using Wasserstein\n approximations

2015/02/08 by Anirban Bhattacharya, Bhattacharya, Anirban, Debdeep Pati +1
Computer Science · Environmental Science · Medicine · #Gaussian Processes and Bayesian Inference #Groundwater flow and contamination studies #Bone health and osteoporosis research

paper · pdf · doi:10.48550/arxiv.1502.02336

Abstract

We study posterior rates of contraction in Gaussian process regression with\nunbounded covariate domain. Our argument relies on developing a Gaussian\napproximation to the posterior of the leading coefficients of a\nKarhunen--Lo 'eve expansion of the Gaussian process. The salient feature of\nour result is deriving such an approximation in the L² Wasserstein distance\nand relating the speed of the approximation to the posterior contraction rate\nusing a coupling argument. Specific illustrations are provided for the Gaussian\nor squared-exponential covariance kernel.\n

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