"Functional and High-dimensional Data Analysis: Regularization, Representation and Regression"

《函数式和高维数据分析：正则化、表示和回归》

• 批准号: 341333-2012
• 负责人: Yao, Fang
• 金额: $ 2.19万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=549321
• 关键词: Functional; dimensional; Data; Analysis; Regularization

Large complex data collected in modern scientific experiments impose tremendous challenges for traditional statistical methods due to high-dimensional and complicated structures. Functional data analysis (FDA) has emerged as a promising field that employs realizations of latent or observed stochastic processes as model units, whose applications are commonly found in many fields, such as longitudinal studies, microarray data, brain images, internet investigations, etc. A fundamental issue of modeling functional data arises from the "curse of dimensionality", as functional objects are conceptually framed as infinite-dimensional processes. This naturally relates to the recently revolutionized area of high-dimensional model selection and regularization.

现代科学实验中采集的大量复杂数据由于其高维、复杂的结构，对传统的统计方法提出了巨大的挑战。功能数据分析（Functional data analysis， FDA）已经成为一个很有前途的领域，它采用潜在的或观察到的随机过程的实现作为模型单元，其应用通常在许多领域，如纵向研究，微阵列数据，脑图像，互联网调查等。建模功能数据的一个基本问题源于“维度的诅咒”，因为功能对象在概念上被框架为无限维的过程。这自然与最近发生革命的高维模型选择和正则化领域有关。