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哪种桥估计量最适合变量选择？AI 解读

We study the problem of variable selection for linear models under the high-dimensional asymptotic setting, where the number of observations $n$ grows at the same rate as the number of predictors $p$. We consider two-stage variable selection techniques (TVS) in which the first stage uses bridge estimators to obtain an estimate of the regression coefficients, and the second stage simply thresholds this estimate to select the “important” predictors. The asymptotic false…

通过近似留一交叉验证高效估计样本外预测误差AI 解读

Summary The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as K-fold cross-validation suffer from large biases. Motivated by the low bias of the leave-one-out cross-validation method, we propose a computationally efficient closed form approximate leave-one-out formula ALO for a large class of regularized estimators. Given the regularized estimate, calculating ALO requires a minor computational…

通过正则化方法的高阶分析克服相变分析的局限AI 解读

We study the problem of estimating a sparse vector $\beta\in\mathbb{R}^{p}$ from the response variables $y=X\beta+w$, where $w\sim N(0,\sigma_{w}^{2}I_{n\times n})$, under the following high-dimensional asymptotic regime: given a fixed number $\delta$, $p\rightarrow\infty$, while $n/p\rightarrow\delta$. We consider the popular class of $\ell_{q}$-regularized least squares (LQLS), a.k.a. bridge estimators, given by the optimization problem \begin{equation*}\hat{\beta}(\lambda,q)\in\arg\min_{\beta}\frac{1}{2}\|y-X\beta\|_{2}^{2}+\lambda\|\beta\|_{q}^{q},\end{equation*}…

LASSO与近似消息传递的调参一致性AI 解读

This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as $n$, the…

LASSO 与近似消息传递的参数一致估计AI 解读

This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as $n$, the…