CAREER: Structured Nonlinear Estimation via Message Passing: Theory and Applications

职业：通过消息传递进行结构化非线性估计：理论与应用

• 批准号: 1254204
• 负责人: Alyson Fletcher
• 金额: $ 50.97万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-03-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1254204&HistoricalAwards=false
• 关键词: CAREER; Structured; Nonlinear; Estimation; via

A fundamental challenge in engineering and science today is that systems contain tremendous numbers of interconnected components with complex interactions. Examples include communication and sensor networks, high-dimensional medical images, or biological systems such as vast sets of interconnected spiking neurons responding to a large array of stimuli. Graphical models provide a probabilistic framework for modeling such systems, and contemporary message-passing algorithms lead to computationally feasible operations by decomposing problems on larger systems into smaller ones. This research develops a broader methodology and new algorithms to address larger classes of more complex nonlinear interconnected systems with potential for great technological impact. For wider dissemination, this is coupled with educational initiatives including developing courses combining perspectives in signal processing, machine learning, and statistics in the context of modern applications. An open-source code base will foster cross-disciplinary research in students, educators, and industry.This research combines the power of high-dimensional graphical models with recent advances in random systems theory to tackle a much wider scope of problems than traditional message-passing or linear methods allow. The investigator addresses the key gaps in scalable estimation and model inference for structured nonlinear systems and develops powerful general algorithms for solving core problems. Four main objectives address aspects of this broader goal: (i) systematic general methods for representing systems characterized by arbitrary interconnections of linear and nonlinear components; (ii) computationally scalable message-passing algorithms for estimation; (iii) rigorous quantification of high-dimensional performance; and (iv) validation of the methods on real data, including neurological system identification. These research thrusts greatly expand the scope of statistical estimation techniques and provide a rigorous approach to large-scale signal processing problems underlying the big data technology of today.

当今工程和科学的一个基本挑战是，系统包含大量具有复杂相互作用的互连组件。 示例包括通信和传感器网络，高维医学图像或生物系统，例如对大量刺激的大量相互联系的尖峰神经元组。 图形模型提供了一个用于建模此类系统的概率框架，并且通过将较大系统上的问题分解为较小的问题，可以通过将问题分解为较小的消息，从而导致计算可行的操作。 这项研究开发了一种更广泛的方法和新算法，以解决具有潜在技术影响的更复杂的非线性互连系统的较大类别。 对于更广泛的传播，这与教育计划相结合，包括开发课程，结合了现代应用程序中信号处理，机器学习和统计数据中的观点。 开源代码基础将促进学生，教育工作者和行业的跨学科研究。这项研究将高维图形模型的力量与随机系统理论的最新进步相结合，以解决与传统消息或线性方法允许的更广泛的问题范围。 研究者解决了结构化非线性系统的可扩展估计和模型推断的关键差距，并开发了解决核心问题的强大一般算法。 四个主要目标解决了这一更广泛目标的方面：（i）代表以线性和非线性组件的任意互连为特征的系统的系统一般方法； （ii）用于估计的计算可扩展的消息通讯算法； （iii）严格量化高维性能； （iv）对实际数据的方法验证，包括神经系统识别。 这些研究强烈扩大了统计估计技术的范围，并为当今大数据技术的大规模信号处理问题提供了严格的方法。