New set-theoretic tools for statistical learning

用于统计学习的新集合论工具

• 批准号: 261450-2012
• 负责人: Pestov, Vladimir
• 金额: $ 1.6万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=594568
• 关键词: New; set; theoretic; tools; statistical

Statistical machine learning theory is a major research direction in computer science, providing a concentual framework for such applications as pattern recognition, classification, and data mining. The theory is using a wide variety of mathematical tools, primarily probability theory and statistics, as well as modern functional analysis, combinatorics, and geometry. In this proposal, we aim to address some open problems of statistical learning using tools of set theory, logic, and set-theoretic topology that have not been previously applied. Here are some of the problems we want to focus on.

统计机器学习理论是计算机科学的一个重要研究方向，为模式识别、分类和数据挖掘等应用提供了一个概念框架。该理论使用了各种各样的数学工具，主要是概率论和统计学，以及现代泛函分析，组合学和几何学。在这个建议中，我们的目标是解决一些开放的问题，统计学习使用的工具集理论，逻辑和集理论拓扑结构，以前没有应用。以下是我们要关注的一些问题。