CIF: Small: Sparsity and Scarcity in High-Dimensional Point Processes

CIF：小：高维点过程中的稀疏性和稀缺性

• 批准号: 1319927
• 负责人: Rebecca Willett
• 金额: $ 38.63万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2014-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1319927&HistoricalAwards=false
• 关键词: CIF; Small; Sparsity; Scarcity; Dimensional

A wide variety of important applications rely upon our ability to quickly and accurately understand the physical world using a meager supply of event-based data. Such data arise when indirect observations of a physical phenomenon are collected by measuring discrete events (such as photons hitting a detector, sequence motifs appearing in a genome, packets traveling through an Internet router, neurons firing, or people interacting in a social network). The challenge here is to use extremely small numbers of random events to perform inference on the underlying high-dimensional phenomenon (e.g., the distribution of tissue in the body or the distribution of traffic in a network). In this case, conventional models of sensing and noise do not apply, and robust inference requires the development of both novel theoretical analyses and new computational methods.Point processes model random processes in which a realization consists of a collection of isolated events distributed across space or time. This research program is aimed at the development of new theory and methods for exploiting low-dimensional or sparse models of high-dimensional signal structure using scarce point process realizations. The theoretical results facilitate characterization of fundamental performance limits, such as bounds on the error of physically realizable models of inverse problems in photon-limited imaging and the performance gap between online and batch processing of streaming data. Furthermore, the methods themselves are practical and resource-efficient in a broad range of contexts, and being used by astronomers, microscopists, social scientists, and geneticists.Underlying these methods are techniques at the intersection of statistical signal processing, learning theory, sparse coding, nonlinear approximation theory, optical engineering, and optimization theory.

各种重要的应用程序都依赖于我们使用微薄的基于事件的数据快速准确地了解物理世界的能力。当通过测量离散事件（例如光子撞击探测器、基因组中出现的序列基序、通过互联网路由器传输的数据包、神经元放电或人们在社交网络中交互）来收集对物理现象的间接观察时，就会产生此类数据。这里的挑战是使用极少量的随机事件来对潜在的高维现象（例如，体内组织的分布或网络中流量的分布）进行推断。在这种情况下，传统的传感和噪声模型不适用，鲁棒推理需要开发新颖的理论分析和新的计算方法。点过程对随机过程进行建模，其中实现由分布在空间或空间中的孤立事件的集合组成。时间。该研究计划旨在开发新的理论和方法，利用稀缺点过程实现来开发高维信号结构的低维或稀疏模型。理论结果有助于表征基本性能限制，例如光子有限成像中逆问题的物理可实现模型的误差界限以及流数据的在线和批处理之间的性能差距。此外，这些方法本身在广泛的背景下实用且资源高效，并被天文学家、显微镜学家、社会科学家和遗传学家使用。这些方法的基础是统计信号处理、学习理论、稀疏编码的交叉技术、非线性逼近理论、光学工程和优化理论。