Research map / Learning theory and algorithms / Sample complexity
Minimax-Optimal Univariate Function Selection in Sparse Additive Models: Rates, Adaptation, and the Estimation-Selection Gap
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Establishes minimax separation rates for univariate function selection in sparse additive models, covering FDR/FNR control and support recovery, and studies adaptation and an estimation-selection gap.
Problem
Variable (univariate function) selection in sparse additive models (SpAM) in high-dimensional settings, where the goal is to identify which component functions are non-zero.
Approach
Derives minimax separation rates for univariate function selection in SpAM from two perspectives, sparse multiple testing (FDR and FNR control) and support recovery (wrong recovery probability), and characterizes a gap between estimation and selection difficulty.
Surprising findings
- A gap between estimation and selection difficulty is reported in the abstract title, though details are not available in the provided text.
Experimental setup
Metrics: FDR FNR wrong recovery probability
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