Sparsity oracle inequalities via l_1 regularization in nonparametric models

这项研究工作的特点稀疏模型恢复一般模型类，广义线性模型和分类扩展现有的结果。 该建议的中心目标是：（a）在高维-低样本量设置中定义稀疏性和目标恢复;（B）在最小假设下，表明经验风险最小化与套索型惩罚允许目标恢复。研究人员提出使用一种新型的预言不等式，以表明惩罚的经验风险最小化适应未知的稀疏性的基础统计模型。特别关注随机设计回归和带拒绝选项的分类。高维数据在许多科学学科中越来越常见，如生物和医学科学。 准确估计和实施用于分析此类数据的复杂统计模型具有挑战性。 这个项目的目的是开发一个统一的理论，用于分析高维数据设置中的计算效率程序。这些技术的有用性将通过应用于基因表达数据和并发EEG / fMRI数据来证明。新采用的分类程序有一个内置的拒绝选项，允许在难以分类的情况下不予决定。这大大提高了误诊后果严重的肿瘤分类的性能。这些程序的软件将在万维网上免费提供。

This research effort characterizes sparse model recovery for general model classes, extending existing results for generalized linear models and in classification. The central goals of this proposal are: (a) to define sparsity and target recovery in high dimensional - low sample size settings; (b) to show that empirical risk minimization with a lasso-type penalty allows for target recovery, under minimal assumptions. The investigators advance the use of a novel type of oracle inequalities to show that the penalized empirical risk minimizers adapt to the unknown sparsity of the underlying statistical model. Special attention is given to random design regression and classification with a reject option.High dimensional data are increasingly common in many scientific disciplines such as biological and medical sciences. Accurate estimation and implementation of complex statistical models used for the analysis of such data are challenging. The aim of this project is to develop a unified theory for the analysis of computationally efficient procedures in high dimensional data settings. The usefulness of these techniques will be demonstrated by applications to gene expression data and concurrent EEG / fMRI data. The newly introduced classification procedures have a built-in reject option that allows for withholding decision in cases that are hard to classify. This greatly improves the performance of tumor classification where the consequences of misdiagnosis are severe. The software for these procedures will be made freely available on the world wide web.