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Nonparametric Regression on Fixed-Cardinality Subsets:Minimax Risk and Random-Design Effects
We study regression with subsets as covariates. The response is an unknown function of the input subset, and observations consist of noisy evaluations at uniformly sampled subsets, each containing exactly \(k\) items from a ground set of size \(d\). This problem arises in combination screening, bund
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