Constructs an efficient mixed test for linear functional testing in sparse regression and proves information-theoretic and low-degree lower bounds on adaptive separation rates for general loadings, with computational hardness evidence via sparse CCA reduction.
aY ℓ=1 exp{sℓUℓ −s 2 ℓ /2} bY j=1 exp{tjVj −t 2 j /2} # . Since(U, V)is centered Gaussian, G(s, t) =E
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Linear Functional Testing with General Loadings in Sparse Regression: Separation Rates and Computational Barriers
Constructs an efficient mixed test for linear functional testing in sparse regression and proves information-theoretic and low-degree lower bounds on adaptive separation rates for general loadings, with computational hardness evidence via sparse CCA reduction.