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Activity Number: 534
Type: Contributed
Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #315532
Title: High-Dimensional Nonparametric Regression with Additive Gaussian Process Priors
Author(s): Surya Tokdar*
Companies: Duke University
Keywords: Nonparametric regression ; Gaussian process ; Large-p small-n ; Minimax Rates ; Posterior Convergence ; Bayesian inference
Abstract:

We develop a new theory and method for additive-interactive regression where total predictor effect equals the sum of smaller interaction effects. We show additive-interactive regression offers attractive minimax error rates over traditional nonparametric multivariate regression in a wide variety of settings, including cases where the predictor count is much larger than the sample size and many of the predictors have important effects on the response, potentially through complex interactions. Next, we present a Bayesian implementation by using an additive Gaussian process prior. Model fitting is done by extending stochastic search variable selection to an ergodic Markov chain sampler in the mould of multiple-try Metropolis over discrete inclusion vectors. The method comes with provable asymptotic guarantees and is also shown to offer state-of-the-art support and interaction recovery while improving dramatically over competitors in terms of prediction accuracy on a diverse set of simulated and real data. Results from real data studies provide strong evidence that the additive-interactive framework is an attractive modeling platform for high-dimensional nonparametric regression.


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