基于Libra：R的高维统计线性化Bregman算法
A Tutorial on Libra: R package for the Linearized Bregman Algorithm in High Dimensional Statistics
摘要：
R包Libra代表高维统计中的线性化Bregman Al-出租m。线性化Bregman算法是一种简单的迭代过程，用于生成模型估计的稀疏正则化路径，最早在图像恢复应用数学中发现，特别适合大规模问题的并行实现。这种算法的极限是一个稀疏限制的梯度下降流，称为逆尺度空间，沿着稀疏模型的parsimonious路径从零模型发展到过度的。在稀疏线性回归中，早停正则化的动态在与LASSO几乎相同的条件下可以证明满足无偏Oracle估计，而后者是有偏的。尽管它们的成功应用，统计一致性理论的动态算法仍然在很大程度上开放，除了最近的一些进展线性回归。在本教程中，将讨论软件包中的算法实现，用于统计学中几种广泛使用的稀疏模型，包括线性回归、逻辑回归和几种图形模型（高斯、伊辛和波茨）。除了仿真实例之外，还展示了各种应用案例，包括来自糖尿病的真实世界数据集，COPSS获奖者的出版物，以及两部中国经典小说《西游记》和《红楼梦》的社交网络。
英文摘要：
The R package, Libra, stands for the LInearized BRegman Al- gorithm in high dimensional statistics. The Linearized Bregman Algorithm is a simple iterative procedure to generate sparse regularization paths of model estimation, which are rstly discovered in applied mathematics for image restoration and particularly suitable for parallel implementation in large scale problems. The limit of such an algorithm is a sparsity-restricted gradient descent ow, called the Inverse Scale Space, evolving along a par- simonious path of sparse models from the null model to over tting ones. In sparse linear regression, the dynamics with early stopping regularization can provably meet the unbiased Oracle estimator under nearly the same condition as LASSO, while the latter is biased. Despite their successful applications, statistical consistency theory of such dynamical algorithms remains largely open except for some recent progress on linear regression. In this tutorial, algorithmic implementations in the package are discussed for several widely used sparse models in statistics, including linear regression, logistic regres- sion, and several graphical models (Gaussian, Ising, and Potts). Besides the simulation examples, various application cases are demonstrated, with real world datasets from diabetes, publications of COPSS award winners, as well as social networks of two Chinese classic novels, Journey to the West and Dream of the Red Chamber.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
