Adaptive dimension reduction with a Gaussian process prior

Details Adaptive dimension reduction with a Gaussian process prior Adaptive dimension reduction with a Gaussian process prior

2011-11-04

arxiv.org/abs/1111.1044v2

Mathematics

Statistics Theory

Scientific paper

In nonparametric regression problems involving multiple predictors, there is typically interest in estimating the multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor) adapting to the unknown dimension and anisotropic smoothness of the true surface. We propose such an approach based on a Gaussian process prior with dimension-specific scalings, which are assigned carefully-chosen hyperpriors. We additionally show that using a homogenous Gaussian process with a single bandwidth leads to a sub-optimal rate in anisotropic cases.

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