Flexible Statistical Modeling

本项目研究使用L1和相关正则化来分析大数据集的方法。坐标下降算法被用来为L1和更具侵略性的凹惩罚回归问题提供一整套的解。应用包括用于非常广泛的数据集的广义线性回归模型，以及用于无向图形模型的结构查找算法。L1正则化也被用来开发高效的凸算法，用于寻找对极大的稀疏填充矩阵的低阶近似(SVD)。这个项目开发了具有广泛应用的工具，这里展示了在医学和商品销售中的应用。现代技术基因组学在几个小时内就能测量到一个人基因组上特定位置的50万个或更多的基因类型。通过对几千个个体进行这样的测量，这个项目开发了更强大的统计工具来识别与阿尔茨海默氏症或乳腺癌等疾病相关的SNP组。在线影迷或购书者经常被要求对他们购买的图书进行评分。尽管每个人只看到很小一部分可供选择，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群体中，这允许他们为尚未见过的产品提供推荐。

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.