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LASSO 及相关估计量的分布鲁棒预测误差AI 解读

We study the classical problem of predicting an outcome variable, Y, using a linear combination of a d-dimensional covariate vector, X. We are interested in linear predictors whose coefficients solve infβ∈Rd(EPn[|Y−X⊤β|r])1/r+δρ(β), where δ>0 is a regularization parameter, ρ:Rd→R+ is a convex penalty function, Pn is the empirical distribution of the data and r≥1. Our main contribution is a new bound on the out-of-distribution prediction error of such estimators. The new…

刻画 SLOPE 的权衡：变分视角与 Donoho–Tanner 极限AI 解读

Sorted ℓ1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this paper, we study how this relatively new regularization technique improves variable selection by characterizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I error and power. Assuming a…