权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

BIGDATA: Collaborative Research: F: Foundations of Nonconvex Problems in BigData Science and Engineering: Models, Algorithms, and Analysis

BIGDATA：协作研究：F：大数据科学与工程中非凸问题的基础：模型、算法和分析

基本信息

批准号：
1632971
负责人：
Jong-Shi Pang
金额：
$ 40.07万
依托单位：
University of Southern California
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-09-01 至 2020-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1632971&HistoricalAwards=false
关键词：
BIGDATA Collaborative Research Foundations Nonconvex

项目摘要

In today's digital world, huge amounts of data, i.e., big data, can be found in almost every aspect of scientific research and human activity. These data need to be managed effectively for reliable prediction and inference to improve decision making. Statistical learning is an emergent scientific discipline wherein mathematical modeling, computational algorithms, and statistical analysis are jointly employed to address these challenging data management problems. Invariably, quantitative criteria need to be introduced for the overall learning process in order to gauge the quality of the solutions obtained. This research focuses on two important criteria: data fitness and sparsity representation of the underlying learning model. Potential applications of the results can be found in computational statistics, compressed sensing, imaging, machine learning, bio-informatics, portfolio selection, and decision making under uncertainty, among many areas involving big data.Till now, convex optimization has been the dominant methodology for statistical learning in which the two criteria employed are expressed by convex functions either to be optimized and/or set as constraints of the variables being sought. Recently, non-convex functions of the difference-of-convex (DC) type and the difference-of-convex algorithm (DCA) have been shown to yield superior results in many contexts and serve as the motivation for this project. The goal is to develop a solid foundation and a unified framework to address many fundamental issues in big data problems in which non-convexity and non-differentiability are present in the optimization problems to be solved. These two non-standard features in computational statistical learning are challenging and their rigorous treatment requires the fusion of expertise from different domains of mathematical sciences. Technical issues to be investigated will cover the optimality, sparsity, and statistical properties of computable solutions to the non-convex, non-smooth optimization problems arising from statistical learning and its many applications. Novel algorithms will be developed and tested first on synthetic data sets for preliminary experimentation and then on publicly available data sets for realism; comparisons will be made among different formulations of the learning problems.

在当今的数字世界中，海量数据，即大数据，几乎可以在科学研究和人类活动的各个方面找到。需要对这些数据进行有效管理，以便进行可靠的预测和推断，从而改进决策。统计学习是一门新兴的科学学科，其中数学建模、计算算法和统计分析被联合用于解决这些具有挑战性的数据管理问题。通常，需要为整个学习过程引入量化标准，以衡量所获得的解决方案的质量。这项研究的重点是两个重要的标准：数据适合性和底层学习模型的稀疏表示。在许多涉及大数据的领域中，这些结果在计算统计、压缩感知、成像、机器学习、生物信息学、投资组合选择和不确定情况下的决策中具有潜在的应用。到目前为止，凸优化一直是统计学习的主要方法，其中所使用的两个准则用凸函数来表示以被优化和/或设置为所求变量的约束。最近，凸差(DC)型非凸函数和凸差算法(DCA)已被证明在许多情况下都能产生优越的结果，并成为本项目的动机。目标是建立一个坚实的基础和统一的框架，以解决大数据问题中的许多基本问题，其中非凸性和不可微性存在于要解决的优化问题中。计算统计学习中的这两个非标准特征具有挑战性，它们的严格处理需要来自数学科学不同领域的专业知识的融合。要研究的技术问题将包括统计学习及其许多应用中产生的非凸、非光滑优化问题的可计算解的最优性、稀疏性和统计性质。新的算法将首先在用于初步实验的合成数据集上开发和测试，然后在用于现实的公开可用数据集上进行测试；将在不同的学习问题公式之间进行比较。