Minimax-optimal nonparametric regression in high dimensions

Journal Article

© Institute of Mathematical Statistics, 2015.Minimax L2 risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on d = O(log n) important predictors among a list of p predictors, with logp = o(n); (2) the true regression surface depends on O(n) predictors but is an additive function where each additive component is sparse but may contain two or more interacting predictors and may have a smoothness level different from other components. For either modeling assumption, a practicable extension of the widely used Bayesian Gaussian process regression method is shown to adaptively attain the optimal minimax rate (up to log n terms) asymptotically as both n,p→∞with logp = o(n).

Full Text

Duke Authors

Cited Authors

  • Yang, Y; Tokdar, ST

Published Date

  • 2015

Published In

Volume / Issue

  • 43 / 2

Start / End Page

  • 652 - 674

International Standard Serial Number (ISSN)

  • 0090-5364

Digital Object Identifier (DOI)

  • 10.1214/14-AOS1289