EAGER: The Exploration of Geometric and Non-Geometric Structure in Data

EAGER：数据中几何和非几何结构的探索

• 批准号: 1550757
• 负责人: Mikhail Belkin
• 金额: $ 15万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2017-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1550757&HistoricalAwards=false
• 关键词: EAGER; Exploration; Geometric; Non; Structure

The goal of machine learning is to extract useful information from data. While the amount of data available to researchers for analysis is ever increasing, much of the data are unlabeled, meaning that the data come without labels indicating their associations with specific learning tasks. Thus understanding unsupervised inference is one of the key problems in machine learning. In addition, data annotated for a certain task may be difficult to use even for tasks only slightly different. This is known as the problem of transfer learning in the literature. To make the most of the available information, machine learning algorithms need to to obtain, analyze and use realistic structural assumptions about the data based on rigorous mathematical models. The proposed work offers students working on this project an opportunity to be exposed to a broad spectrum of topics including machine learning, statistics, geometry and applied mathematics. Students will learn a combination of theory and algorithm development skills in machine learning and data analysis. The results of this work will be disseminated to the broad scientific community through publications in journals, conferences, presentations in various venues, including tutorials and course notes. The material related to this project will be incorporated in PI?s and co-PI's courses. The PIs will also create summer research and practice opportunities for interested undergraduate students in research related to the project. In this EAGER project an exploration of two types of structural assumptions on the data will be started. Geometric structures in data will be explored, such as hierarchical structure of clusters and density. The use of partial orders for non-geometric data will be explored, based on probabilistic models for partial rankings an orders for problems such as zero-shot learning and transfer learning. By approaching the problem of inference from data within these frameworks, output of this project will be a stepping stone to the challenges of machine learning and to developing efficient algorithms to advance the state-of-the-art both in theory and practice. It is argued argue that these models and the proposed mathematical/algorithmic machinery are amenable to theoretical analysis and will provide insight into properties of real data. Results from the proposed work will broaden the scope of machine learning methods to analyze more complex data in a theoretically well-founded manner.

机器学习的目标是从数据中提取有用的信息。 虽然研究人员可用于分析的数据量不断增加，但大部分数据都是未标记的，这意味着数据没有标签，表明它们与特定学习任务的关联。因此，理解无监督推理是机器学习的关键问题之一。 此外，为某个任务注释的数据可能难以使用，即使对于仅略有不同的任务也是如此。 这在文献中被称为迁移学习问题。 为了充分利用可用信息，机器学习算法需要基于严格的数学模型来获取、分析和使用关于数据的现实结构假设。拟议的工作为从事该项目的学生提供了一个接触广泛主题的机会，包括机器学习，统计，几何和应用数学。学生将学习机器学习和数据分析方面的理论和算法开发技能。这项工作的成果将通过在期刊上发表文章、会议、在各种场合的介绍，包括教程和课程说明，向广大科学界传播。 与本项目相关的材料将纳入PI？和Co-PI的课程。PI还将为感兴趣的本科生创造夏季研究和实践机会，以进行与该项目相关的研究。在这个EAGER项目中，将开始探索两种类型的数据结构假设。 将探索数据中的几何结构，例如聚类和密度的层次结构。将探索使用非几何数据的偏序，基于概率模型的部分排名和零射击学习和迁移学习等问题的顺序。通过解决这些框架内的数据推理问题，该项目的输出将成为机器学习挑战的垫脚石，并开发有效的算法，以在理论和实践上推进最先进的技术。 有人认为，这些模型和建议的数学/算法的机器是服从理论分析，并将提供洞察真实的数据的属性。拟议工作的结果将扩大机器学习方法的范围，以理论上有根据的方式分析更复杂的数据。