Minimax Additive Regression under Unknown Dependent Designs
Researchers prove minimax rates for additive regression when dimension grows and the design may be dependent.
The paper studies additive regression when the random design on the unit cube may be dependent and the dimension can grow with the sample size. It defines coupled smoothness classes, adapts a Riesz-basis construction for functional ANOVA, and analyzes thresholded least-squares estimators. Matching minimax upper and lower bounds are given for prediction with known or unknown marginal densities, and centered additive components can be recovered at the same aggregate rate.
- Studies additive regression on dependent designs as dimension grows with n.
- Coupled smoothness classes separate density regularity from additive components.
- Thresholded least-squares estimators match minimax prediction bounds.
- Unknown densities match known-density rates when they are smooth enough.
From the original article
1 min read at arxiv.orgWe study additive regression under a potentially non-product random design on $[0,1]^d$, allowing the dimension $d$ to grow with the sample size $n$. We introduce coupled smoothness classes that separately control the regularity of the marginal densities and the density-weighted additive components.
By Baptiste Ferrere · arxiv.org
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