Flexible Statistical Modeling

本项目研究使用L1和相关正则化分析大型数据集的方法。坐标下降算法的发展，以提供整个家庭的解决方案，L1和更积极的凹惩罚回归问题。应用程序包括广义线性回归模型的非常广泛的数据集，和结构发现算法的无向图形模型。L1正则化也被用来开发高效的凸算法，用于寻找超大型稀疏矩阵的低秩近似（SVD）。该项目开发了具有广泛应用的工具，如医学和商品销售。现代基因组学技术可以在几个小时内测量出个体基因组沿着特定位置（SNPs）的50多万种基因型。通过对几千名个体（有些是病人，有些是健康人）进行这样的测量，该项目开发了强大的统计工具，用于识别与阿尔茨海默氏症或乳腺癌等疾病相关的SNPs组。在线电影租赁者或图书购买者经常被要求评价他们的购买。尽管每个人看到的是这些选择中的一小部分，但研究人员能够开发出推荐系统，利用重叠来学习电影类型，并将观众分配到志同道合的团体，并允许他们为尚未看到的产品提供推荐。

This project studies methods for analyzing large datasets using L1 andrelated regularization. Coordinate descent algorithms are developed toprovide entire families of solutions for L1 and more aggressiveconcave penalized regression problems. Applications includegeneralized linear regression models for very wide datasets, andstructure-finding algorithms for undirected graphical models. L1regularization is used as well to develop efficient convex algorithmsfor finding low-rank approximations (SVDs) to extremely large,sparsely populated matrices.This project develops tools with a wide variety of applications,illustrated here in medicine and merchandising. Modern technologies ingenomics produce measurements of half a million or moregenotypes at particular locations (SNPs) along an individual's genomein a few hours. Armed with such measurements on a few thousandindividuals, some sick and some healthy, this project developspowerful statistical tools for identifying groups of SNPs associatedwith diseases such as Alzheimer's or breast cancer. Online movierenters or book buyers are often asked to rate theirpurchases. Although each individual sees a minuscule fraction of theselections available, the investigators are able to developrecommender systems that exploit the overlap to learn genres ofmovies, and assign viewers to like-minded cliques, and which allowthem to make recommendations for products not yet seen.