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Lambert 惩罚：稀疏回归的对数收缩AI 解读

Sparse regression must balance prediction accuracy with reproducible variable selection. We introduce the Lambert penalty by limiting how quickly the retained fraction of a scalar score increases after variable entry. Maximizing retention under this scale-equivariant constraint yields a logarithmic transition from exact zero to an identity tail. The bounded penalty has a fixed shape and a single penalty parameter selected by training-only five-fold cross-validation. We…

超高维回归中最大检验校准的 Stein 收缩与诚实子模型选择AI 解读

Classical preliminary-test and Stein-type estimators interpolate between restricted and full regression fits, but OLS and chi-squared calibration fail when $p\gg n$ and the restriction is data-adaptive. We propose an honest sample-separated framework built around a common selected-null law. Independent selection data extend a mandatory core; separate estimation data pair a complete-design regularized full-model (FM) fit with a fresh exact-null submodel refit. A maximum…