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.

各种各样的重要应用都依赖于我们使用少量基于事件的数据快速准确地理解物理世界的能力。当通过测量离散事件（例如光子击中探测器，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互动）收集对物理现象的间接观察时，就会产生这种数据。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，身体中组织的分布或网络中业务的分布）。在这种情况下，传统的感知和噪声模型不再适用，鲁棒推理需要发展新的理论分析和新的计算方法。点过程模拟随机过程，其中实现由分布在空间或时间上的孤立事件的集合组成。该研究计划旨在开发新的理论和方法，利用稀缺的点过程实现来利用高维信号结构的低维或稀疏模型。理论结果有利于表征的基本性能限制，如光子限制成像的逆问题的物理可实现的模型的错误和性能之间的差距在线和批量处理流数据的界限。此外，这些方法本身在广泛的背景下是实用的和资源有效的，并且被天文学家、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、非线性逼近理论、光学工程和优化理论的交叉技术。