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.

依赖性的度量在发现变量之间的关联从而导致科学发现方面发挥着核心作用。在实践中，分析师需要从数据中计算这些指标，这可能具有挑战性。例如，当数据具有连续和离散变量的混合时，或者当数据位于具有丰富边界的复杂空间时，标准估计量可能会失败。这个项目的目的是解决实际问题，估计措施的依赖关系，并提供新的估计，以克服这些挑战。所提出的工作的成功将导致新的估计发现新的方面的数据。直接影响是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;持久的影响将在不同的领域，包括基因组学，生物学，机器学习和人工智能。该项目还通过开设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：设计新的估计信息理论措施和设计新的估计现代措施的相关性，被定义为一个解决方案的优化问题。在前者中，解决了两个主要的挑战：混合类型（连续和离散）和边界偏差的变量。借用当地的对数似然密度估计，最近邻方法和顺序统计的技术，这导致了一个新的估计，可以适应当地的几何分布的原则性的方式，显着改善现有的估计。在现代数据分析中，一些相关性的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。该建议旨在提供一个原则性的方法，并提出一个新的估计借用重要性抽样和最近邻方法的见解。所提出的框架被施加到估计hyperconstitutivity比，信息理论的数量，捕捉隐藏的相关性的数据，自然被定义为一个无限维优化的解决方案。建议的措施hypercontractivity发现潜在的相关性，其他标准的措施是不能够，在典型的合成例子和真实的dataset.This奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。