CIF: RI: Small: Information-theoretic measures of dependencies and novel sample-based estimators

CIF：RI：小：依赖性的信息论测量和新颖的基于样本的估计器

• 批准号: 1815535
• 负责人: Sewoong Oh
• 金额: $ 45万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-15 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1815535&HistoricalAwards=false
• 关键词: CIF; RI; Small; Information; theoretic

Measures of dependencies play central roles in discovering associations between variables that leads to scientific discoveries. In practice, analysts need to compute these measures from data, which can be challenging. The standard estimators can fail when, for example, the data has a mixture of continuous and discrete variables, or when the data lies on a complex space with abundant boundaries. The aim of this project is to address practical issues in estimating measures of dependencies, and provide novel estimators to overcome these challenges. The success of the proposed work will result in novel estimators for discovering new aspects of data. The immediate impact is in two specific contexts: discovering correlations in biological datasets and analyzing the inner-workings of deep neural networks; the lasting impact will be in diverse fields including genomic, biology, machine learning, and artificial intelligence. This project also integrates research with education through the creation of a graduate course on statistical learning. In addition, the project will offer undergraduates the opportunity to be involved in research.This proposal addresses two fundamental questions: designing novel estimators for information theoretic measures and designing novel estimators for modern measures of correlation that is defined as a solution of optimization problems. In the former, two major challenges are addressed: variables of mixed type (continuous and discrete) and boundary biases. Borrowing techniques from local log-likelihood density estimators, nearest neighbor methods, and order statistics, this leads to a new estimator that can adapt to the local geometry of the distributions in a principled way, that improves significantly over existing estimators. In modern data analysis, several measures of correlations are naturally defined as solutions of optimization problems, making them challenging to estimate. This proposal aims to provide a principled approach and propose a new estimator borrowing insights from importance sampling and nearest neighbor methods. The proposed framework is applied to estimate hypercontractivity ratio, an information theoretic quantity that captures hidden correlations in the data and is naturally defined as a solution of an infinite dimensional optimization. The proposed measure of hypercontractivity is shown to discover potential correlations that other standard measures are not able to, in canonical synthetic examples and real datasets.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

依赖性测量在发现导致科学发现的变量之间的关联方面发挥着核心作用。在实践中，分析师需要根据数据计算这些指标，这可能具有挑战性。例如，当数据混合有连续变量和离散变量时，或者当数据位于具有丰富边界的复杂空间时，标准估计器可能会失败。该项目的目的是解决估计依赖性度量的实际问题，并提供新颖的估计器来克服这些挑战。拟议工作的成功将产生新的估计器来发现数据的新方面。直接影响体现在两个特定的背景下：发现生物数据集中的相关性和分析深度神经网络的内部工作原理；持久的影响将遍及基因组学、生物学、机器学习和人工智能等各个领域。该项目还通过创建统计学习研究生课程将研究与教育结合起来。此外，该项目将为本科生提供参与研究的机会。该提案解决了两个基本问题：为信息论测量设计新颖的估计器，以及为定义为优化问题解决方案的现代相关性测量设计新颖的估计器。前者解决了两个主要挑战：混合类型变量（连续和离散）和边界偏差。借用局部对数似然密度估计器、最近邻方法和阶次统计的技术，这产生了一种新的估计器，它可以以原则性的方式适应分布的局部几何形状，比现有的估计器有显着改进。在现代数据分析中，多种相关性度量自然被定义为优化问题的解决方案，这使得它们难以估计。该提案旨在提供一种原则性方法，并借鉴重要性采样和最近邻方法的见解，提出一种新的估计器。所提出的框架用于估计超收缩率，这是一种捕获数据中隐藏相关性的信息理论量，并且自然地定义为无限维优化的解决方案。所提议的超收缩性测量结果表明，在规范的综合示例和真实数据集中，可以发现其他标准测量方法无法发现的潜在相关性。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的评估进行评估，被认为值得支持。影响审查标准。