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

各种各样的重要应用依赖于我们使用少量的基于事件的数据快速而准确地理解物理世界的能力。当通过测量离散事件(例如击中探测器的光子、基因组中出现的序列基序、通过互联网路由器传输的信息包、神经元激活或人在社交网络中的互动)来收集对物理现象的间接观察时，就会产生这样的数据。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的流量分布)进行推断。在这种情况下，传统的感知和噪声模型不适用，稳健推理需要发展新的理论分析和新的计算方法。点过程建模随机过程，其中实现由分布在空间或时间上的孤立事件的集合组成。这项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的性能极限，例如光子受限成像中反问题的物理可实现模型的误差界限，以及在线和批处理流数据之间的性能差距。此外，这些方法本身在广泛的背景下是实用的和资源高效的，被天文学家、微观学家、社会科学家和遗传学家使用。这些方法背后是统计信号处理、学习理论、稀疏编码、非线性逼近理论、光学工程和最优化理论的交叉技术。

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.