Complex system and structure modeling by data processing

本文的研究重点是数据驱动的结构建模。随着计算技术在存储和处理大量复杂结构数据方面的进步，不可避免地需要将可用的数据快速转换为关于其底层结构的适当信息。将数据转换为结构的一个重要挑战是参数建模的顺序选择。在过去的几十年里，各种参数模型复杂性选择方法被提出，我最近针对这个问题开发了一种新的方法。该方法利用了传统系统辨识(存在未建模动态等问题)和计算学习理论的思想，并利用信息论中的编码概念从一个新的角度来处理模型选择问题。新方法的这些特点使该方法的推广远远超出了最初的应用。拟议的项目侧重于新复杂性选择方法在理论、方法论和应用方面的相关发展。随着控制的现代观点将反馈系统视为不确定性处理和管理的工具，提供数据驱动结构和不确定性建模的兼容方法变得越来越重要。新的复杂性选择方法的主要优势在于它能够量化结构的主要不确定性。本研究的目标是在非线性结构建模、自适应和在线系统建模与辨识、ARMAX建模等领域开发和扩展数据驱动结构建模的新方法。新方法的巨大优势，从其一致的理论到其有效的算法，有望在各种潜在的应用中广泛使用，包括生物医学系统识别和建模、生物信息学、通信中的信道识别和经济学。

This research focuses on data-driven structure modeling. As computational technology advances in storing and processing large amounts of complex-structured data, there is an inevitable demand for fast transformation of the available data to proper information about its underlying structure. One important challenge in transforming data to structure is in order selection for parametric modeling. Over the past decades,  various parametric model complexity selection approaches have been proposed  and  I have recently developed a new approach for this problem. The new approach employs ideas of conventional system identification (with issues such as unmodeled dynamics) and computational learning theory, and also utilizes coding concepts of information theory to approach the model selection problem from a new perspective. These characteristics of the new approach allow the method to spread far beyond its initial applications. The proposed project focuses on related developments in theory, methodology, and application of the new complexity selection approach. As the control's modern view sees feedback systems as tools for uncertainty handling and management, it is becoming more and more essential to provide compatible methods of data-driven structure and uncertainty modeling. The main advantage of the new complexity selection approach is in its ability to quantify the structure's  uncertainty. The objectives of this research are to develop and expand the new approach for data-driven structure modeling in areas such as nonlinear structure modeling, adaptive and online system modeling and identification, and ARMAX modeling. The great strength of the new approach, from its consistent theory to its effective algorithms, promises a broad use of these methods in a variety of potential applications including biomedical system identification and modeling, bioinformatics, channel identification in communications, and economics.