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模型搜索后的预测误差AI 解读

Estimation of the prediction error of a linear estimation rule is difficult if the data analyst also uses data to select a set of variables and constructs the estimation rule using only the selected variables. In this work, we propose an asymptotically unbiased estimator for the prediction error after model search. Under some additional mild assumptions, we show that our estimator converges to the true prediction error in $L^{2}$ at the rate of $O(n^{-1/2})$, with $n$ being…

利用平方根套索进行未知方差下的选择后推断AI 解读

There has been much recent work on inference after model selection in situations where the noise level is known. However, the error variance is rarely known in practice and its estimation is difficult in high-dimensional settings. In this work we propose using the square-root lasso, also known as the scaled lasso, to perform inference for selected coefficients and the noise level simultaneously. The square-root lasso has the property that the choice of a reasonable tuning…

基于随机化响应的选择后推断AI 解读

Inspired by sample splitting and the reusable holdout introduced in the field of differential privacy, we consider selective inference with a randomized response. We discuss two major advantages of using a randomized response for model selection. First, the selectively valid tests are more powerful after randomized selection. Second, it allows consistent estimation and weak convergence of selective inference procedures. Under independent sampling, we prove a selective (or…