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高斯混合模型的稳健无监督多任务与迁移学习AI 解读

Unsupervised learning has been widely used in many real-world applications. One of the simplest and most important unsupervised learning models is the Gaussian mixture model (GMM). In this work, we study the multi-task learning problem on GMMs, which aims to leverage potentially similar GMM parameter structures among tasks to obtain improved learning performance compared to single-task learning. We propose a multi-task GMM learning procedure based on the EM algorithm that…

关于《统计学家的共同被引与共同署名网络》的讨论AI 解读

We congratulate the authors for their stimulating and thought-provoking work on network data analysis. In the article, the authors not only introduce a new large-scale and high-quality publication dataset that will surely become an important benchmark for further network research, but also present novel statistical methods and modeling which lead to very interesting findings about the statistics community. There is much material for thought and exploration. In this…

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*}…