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以正则化最小二乘统一模型选择与稀疏恢复AI 解读

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least squares with concave penalties. For model selection, we establish conditions under which a regularized least squares estimator enjoys a nonasymptotic property, called the weak oracle property, where the dimensionality can grow exponentially…

DASSO：Dantzig 选择器与 Lasso 的联系AI 解读

Summary We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the least angle regression algorithm that is used to compute the lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to the least angle regression algorithm. Comparison of the two algorithms sheds new light on the question of how the lasso and Dantzig…

超高维特征空间的确定性独立筛选AI 解读

Summary Variable selection plays an important role in high dimensional statistical modelling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, accuracy of estimation and computational cost are two top concerns. Recently, Candes and Tao have proposed the Dantzig selector using L1-regularization and showed that it achieves the ideal risk up to a logarithmic factor log(p). Their innovative…

使用因子模型估计高维协方差矩阵AI 解读

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to [infinity] as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observable and the number of factors K is allowed to grow with p. We investigate…

讨论：变量数远大于样本量时的 Dantzig 选择器统计估计AI 解读

Professors Candès and Tao are to be congratulated for their innovative and valuable contribution to high-dimensional sparse recovery and model selection.The analysis of vast data sets now commonly arising in scientific investigations poses many statistical challenges not present in smaller scale studies.Many of these data sets exhibit sparsity where most of the data corresponds to noise and only a small fraction is of interest.The needs of this research have excited much…