Lower bounds on minimax rates for nonparametric regression with additive sparsity and smoothness

NeurIPS 2009 Garvesh RaskuttiBin YuMartin J. Wainwright

This paper uses information-theoretic techniques to determine minimax rates for estimating nonparametric sparse additive regression models under high-dimensional scaling. We assume an additive decomposition of the form $f^*(X_1, \ldots, X_p) = \sum_{j \in S} h_j(X_j)$, where each component function $h_j$ lies in some Hilbert Space $\Hilb$ and $S \subset \{1, \ldots, \pdim \}$ is an unknown subset with cardinality $\s = |S$... (read more)

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