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

当今工程和科学领域的一个基本挑战是，系统包含大量相互关联的组件，这些组件之间存在复杂的相互作用。例子包括通信和传感器网络，高维医学图像，或生物系统，如大量相互连接的尖峰神经元对大量刺激做出反应。图形模型为这类系统的建模提供了一个概率框架，而当代的消息传递算法通过将大系统上的问题分解成小系统，导致计算上可行的操作。本研究开发了一种更广泛的方法和新的算法来解决更复杂的非线性互联系统的更大类别，具有巨大的技术影响潜力。为了更广泛的传播，这与教育活动相结合，包括在现代应用背景下开发结合信号处理、机器学习和统计学观点的课程。开源代码库将促进学生、教育者和工业界的跨学科研究。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展相结合，以解决比传统的消息传递或线性方法所允许的更广泛的问题。研究者解决了结构化非线性系统在可扩展估计和模型推理方面的关键差距，并为解决核心问题开发了强大的通用算法。四个主要目标涉及这一更广泛目标的各个方面：(i)表示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）用于估计的可计算扩展的消息传递算法；（iii）严格量化高维性能；（iv）在真实数据上验证方法，包括神经系统识别。这些研究重点极大地扩展了统计估计技术的范围，并为当今大数据技术基础上的大规模信号处理问题提供了严格的方法。

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.