Publications [#258730] of Surya T. Tokdar
Papers Published
- Yang, Y; Tokdar, ST, Minimax-optimal nonparametric regression in high dimensions,
Annals of Statistics, vol. 43 no. 2
(2015),
pp. 652-674, Institute of Mathematical Statistics, ISSN 0090-5364 [doi]
(last updated on 2024/04/24)Abstract:
© 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).