Collaborative Research: Statistical Estimation with Algebraic Structure

合作研究：代数结构的统计估计

基本信息

批准号：
1712730
负责人：
Alexander Wein
金额：
$ 28万
依托单位：
New York University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-07-01 至 2021-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712730&HistoricalAwards=false
关键词：
Collaborative Research Statistical Estimation Algebraic

项目摘要

Scientific and engineering disciplines ranging from structural biology to computer vision rely on data collection and analysis to guide scientific discovery. Critically, in such applications, the systems under study constrain and govern the structure of information in collected data. The goal of this research project is to develop a family of statistical models that enables a systematic extraction of relevant statistical information from these datasets by bringing together interdisciplinary concepts from statistics and optimization. The approach under development aims to provide a new set of statistical tools that is adapted to this class of problems and that could have a transformative impact on several scientific disciplines.This project is articulated around a core set of techniques to analyze datasets in the context of a latent algebraic structure, often arising from the physical laws underlying the data collection processes. Unlike more traditional statistical problems where a linear underlying structure is often built into the model, data-driven science generates problems with algebraic but often non-linear structure. The project focuses on problems of central importance in a variety of scientific and engineering disciplines, including signal processing, structural biology, and computer vision, that share a similar feature: the need to leverage algebraic structure in order to extract information from data. The project aims at developing a systematic approach to analyze this family of problems, together with a general procedure to construct computationally efficient algorithms using low-rank tensor decomposition. Importantly, these methods can be proved to be statistically optimal and therefore make the most efficient use of collected data.

从结构生物学到计算机视觉的科学和工程学科依靠数据收集和分析来指导科学发现。至关重要的是，在此类应用中，所研究的系统限制和管理所收集数据中的信息结构。该研究项目的目标是开发一系列统计模型，通过汇集统计和优化的跨学科概念，能够从这些数据集中系统地提取相关统计信息。正在开发的方法旨在提供一套新的统计工具，适用于此类问题，并可能对多个科学学科产生变革性影响。该项目围绕一组核心技术进行阐述，以在以下背景下分析数据集：潜在的代数结构，通常由数据收集过程背后的物理定律产生。与模型中通常内置线性基础结构的传统统计问题不同，数据驱动的科学产生具有代数但通常是非线性结构的问题。该项目重点关注各种科学和工程学科中的核心问题，包括信号处理、结构生物学和计算机视觉，这些学科具有相似的特征：需要利用代数结构从数据中提取信息。该项目旨在开发一种系统方法来分析这一系列问题，以及使用低秩张量分解构建计算高效算法的通用程序。重要的是，这些方法可以被证明在统计上是最佳的，因此可以最有效地利用收集的数据。

项目成果

期刊论文数量（18）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Sum-of-Squares Optimization and the Sparsity Structure of Equiangular Tight Frames

等角紧框架的平方和优化与稀疏结构

DOI：
10.1109/sampta45681.2019.9030987
发表时间：
2019-01-30
期刊：
2019 13th International conference on Sampling Theory and Applications (SampTA)
影响因子：
0
作者：
A. B;eira;eira;Dmitriy Kunisky
通讯作者：
Dmitriy Kunisky

Spectral methods from tensor networks

张量网络的谱方法