Optimal Modeling in Curved Reproducing Kernel Hilbert Spaces

曲线再生核希尔伯特空间中的最优建模

• 批准号: 0601271
• 负责人: Jose Principe
• 金额: $ 24万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0601271&HistoricalAwards=false
• 关键词: Optimal; Modeling; Curved; Reproducing; Kernel

Principe AbstractThe objective of this research is to understand further the optimization of nonlinear systems with cost functions based on information theory. The recent interpretation of entropy as the mean square of the projected samples in feature space provides a link to the theory of reproducing kernels Hilbert spaces (RKHS), and raises the hypothesis that it may be possible to analytically compute the optimal solution of nonlinear systems, unlike the current estimates that use search procedures. The solution of the two most widely used models in filtering, the Wiener and the Kalman filters will be addressed. The approach is also novel because it will exploit both the inner product structure of the RKHS and the geometry of the estimation process using a differential geometry approach. Intellectual Merits. The intellectual merit of the proposal is to propose a new methodology based on information geometry to adapt systems with cost functions that directly manipulate information in the data, with the expected outcome of improving performance over the conventional methods in creating models from data and providing understanding of data. Broader Benefits. Our technology driven world is creating data at alarming rates. However, humans are interested in information, not data, and this is creating a tremendous bottleneck in medicine, business and even in engineering. Adaptive systems are one of the most promising methods to create models from data and provide understanding. The PI will also educate a breed of graduate students in the new area of differential geometry applied to signal processing who are needed to help solve this information bottleneck.

本研究的目的是进一步理解基于信息论的非线性系统的优化问题。最近的解释熵的投影样本在特征空间的均方提供了一个链接到再生核希尔伯特空间（RKHS）的理论，并提出了一个假设，它可能是分析计算的最佳解决方案的非线性系统，不像目前的估计，使用搜索程序。两个最广泛使用的模型在过滤，维纳和卡尔曼滤波器的解决方案将得到解决。该方法也是新颖的，因为它将利用RKHS的内积结构和使用微分几何方法的估计过程的几何形状。智力优势。 该提案的智力价值是提出一种基于信息几何的新方法，以适应具有直接操纵数据中信息的成本函数的系统，预期结果是在从数据创建模型和提供对数据的理解方面提高传统方法的性能。更广泛的利益。我们的技术驱动的世界正在以惊人的速度创建数据。然而，人类感兴趣的是信息，而不是数据，这在医学、商业甚至工程领域都造成了巨大的瓶颈。自适应系统是从数据创建模型并提供理解的最有前途的方法之一。PI还将在微分几何应用于信号处理的新领域中培养一批研究生，他们需要帮助解决这一信息瓶颈。