EAGER: Theoretic Structures of High Dimensional Data Decomposition

EAGER：高维数据分解的理论结构

• 批准号: 1644588
• 负责人: Lizhong Zheng
• 金额: $ 20万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1644588&HistoricalAwards=false
• 关键词: EAGER; Theoretic; Structures; Dimensional; Data

This project aims at developing an information theoretic view of the problems of dimension reduction and feature selection. The problem of feature selection is a core issue in processing high dimensional data. It is difficult from an information processing point-of-view mainly because when reducing high dimensional data into lower dimensional feature space, it is in general inevitable to incur irreversible information losses. In this work, the problem is formulated as a general lossy information processing problem. The solutions to this problem is efficient algorithms that can be used to choose informative features that are relevant universally to a family of inference tasks.The goal of a general theoretic framework to this problem is to develop systematic understanding and uniform performance comparisons to the existing wide variety of practical solutions. The main technical merit lies in a new operational meaning of information metrics, which connects a large body of research on information theory to the challenges of high dimensional data analytics. A new geometric analysis approach is used in this work, which helps to visualize the problem of feature selections, and link the problem to the well-studied concept of the Hirschfeld-Gebelein-Renyi maximal correlation.The key advantage of the proposed approach is its generality. It can be applied to any type of data, incorporate prior knowledge and side information, connect multiple platforms, follow computation and storage constraints, adapt to time-variations, etc., all based on the same theoretic principle. It is envisioned that such universality would lead to architectural changes in the area of data analysis, with a universal interface that separates the task of a data scientist, in information extraction, from the task of a specialist with domain knowledge, in collecting the data, providing the models, and interpreting the result.

该项目旨在发展降维和特征选择问题的信息论观点。特征选择问题是处理高维数据的核心问题。从信息处理的角度来看，这很困难，主要是因为当将高维数据减少到较低维特征空间时，通常不可避免地会导致不可逆的信息损失。在这项工作中，该问题被表述为一般有损信息处理问题。这个问题的解决方案是有效的算法，可以用来选择与一系列推理任务普遍相关的信息特征。这个问题的通用理论框架的目标是发展系统的理解和与现有的各种实际解决方案的统一性能比较。主要技术优点在于信息度量的新操作意义，它将信息论的大量研究与高维数据分析的挑战联系起来。这项工作中使用了一种新的几何分析方法，这有助于可视化特征选择问题，并将问题与经过深入研究的 Hirschfeld-Gebelein-Renyi 最大相关性概念联系起来。该方法的主要优点是其通用性。它可以应用于任何类型的数据，结合先验知识和辅助信息，连接多个平台，遵循计算和存储约束，适应时间变化等，所有这些都基于相同的理论原理。预计这种通用性将导致数据分析领域的架构变化，通过通用接口将数据科学家的信息提取任务与具有领域知识的专家收集数据、提供模型和解释结果的任务分开。