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• W3105189648 abstract "Minimax $L_2$ 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 $log p=o(n)$; (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 $n,ptoinfty$ with $log p=o(n)$." @default.
• W3105189648 created "2020-11-23" @default.
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• W3105189648 date "2015-04-01" @default.
• W3105189648 modified "2023-09-30" @default.
• W3105189648 title "Minimax-optimal nonparametric regression in high dimensions" @default.
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• W3105189648 doi "https://doi.org/10.1214/14-aos1289" @default.
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