Multiscale Generalized Correlation: A Unified Distance-Based Correlation Measure for Dependency Discovery

多尺度广义相关性：用于依赖性发现的统一的基于距离的相关性测量

• 批准号: 1712947
• 负责人: Cencheng Shen
• 金额: $ 20万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2019-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712947&HistoricalAwards=false
• 关键词: Multiscale; Generalized; Correlation; Unified; Distance

Detecting relationships between two data sets has long been one of the most important questions in statistics and is fundamental to scientific discovery in the big-data era. By developing an open-source, robust, efficient, and scalable statistical methodology for testing dependence on modern data, this project aims to advance the understanding and utility of testing dependence, tackle a number of related statistical inference questions, and accelerate a broad range of data-intensive research. The project incorporates fundamental research in mathematics, statistics, and computer science to further develop a multiscale generalized correlation framework to enable discovery and decision-making via analysis of large and complex data. The tools under development will allow scientists to better explore and understand high-dimensional, nonlinear, and multi-modal data in a myriad of applications. The project aims to provide a unified framework for discovery of relationships between observations in an efficient and theoretically-sound manner. Combining the notion of generalized correlation with the locality principle, multiscale generalized correlation (MGC) is a superior correlation measure that equals the optimal local correlation among all possible local scales. By building upon distance correlation and making use of nearest neighbors, the resulting MGC test statistic is a unique dependence measure that is consistent for testing against all dependencies with finite second moment, and it exhibits better performance than existing state-of-art methods under a wide variety of nonlinear and high-dimensional dependencies. By investigating the theoretical aspects of distance-based correlations, this project aims to further improve the finite-sample performance of MGC-style tests, extend its capability to testing dependence on network and kernel data, and broaden its utility to general inferential questions beyond dependence testing such as two-sample testing, outlier detection, and feature screening, as well as applications to brain activity, networks, and text analysis. Overall, this project intends to establish a unified methodology framework for statistical testing in high-dimensional, noisy, big data, through theoretical advancements, comprehensive simulations, and real data experiments.

检测两个数据集之间的关系长期以来一直是统计中最重要的问题之一，对于大数据时代的科学发现至关重要。通过开发一种开源，健壮，有效和可扩展的统计方法来测试对现代数据的依赖，该项目旨在提高测试依赖性的理解和实用性，解决许多相关的统计推断问题，并加速一系列数据密集型研究。该项目结合了数学，统计学和计算机科学方面的基本研究，以进一步开发多尺度的广义相关框架，以通过大型和复杂数据的分析来实现发现和决策。所开发的工具将使科学家能够更好地探索和理解无数应用程序中的高维，非线性和多模式数据。该项目旨在提供一个统一的框架，以有效和理论上的方式发现观察之间的关系。将广义相关性的概念与位置原理相结合，多尺度广义相关性（MGC）是一种优越的相关度量，它等于所有可能的局部尺度之间的最佳局部相关性。通过建立距离相关性并利用最近的邻居，由此产生的MGC测试统计量是一种独特的依赖度量，对于对所有有限第二时刻的所有依赖性测试都是一致的，并且比在各种非线性和高维依赖性下的现有最先进方法表现出更好的性能。通过调查基于距离的相关性的理论方面，该项目旨在进一步提高MGC式测试的有限样本性能，将其能力扩展到测试对网络和内核数据的依赖性，并将其效用扩大到一般推论问题，而不是依赖性测试，例如二次样本测试，远程测试，概述筛选，并进行筛选，并进行分析，并进行分析，并进行分析，并进行了细分，以及大脑的应用程序，以及对大脑进行分析。总体而言，该项目打算通过理论进步，全面的模拟和实际数据实验建立一个统一的方法框架，以在高维，嘈杂，大数据中进行统计测试。

项目成果

Discovering and deciphering relationships across disparate data modalities

• DOI: 10.7554/elife.41690
• 发表时间: 2019-01-15
• 期刊: ELIFE
• 影响因子: 7.7
• 作者: Vogelstein, Joshua T.;Bridgeford, Eric W.;Shen, Cencheng
• 通讯作者: Shen, Cencheng

From Distance Correlation to Multiscale Graph Correlation

• DOI: 10.1080/01621459.2018.1543125
• 发表时间: 2019-04-08
• 期刊: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• 影响因子: 3.7
• 作者: Shen, Cencheng;Priebe, Carey E.;Vogelstein, Joshua T.
• 通讯作者: Vogelstein, Joshua T.