New set-theoretic tools for statistical learning

统计机器学习理论是计算机科学的一个主要研究方向，为模式识别、分类和数据挖掘等应用提供了一个统一的框架。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。在本提案中，我们的目标是使用集合论、逻辑和集合论拓扑的工具来解决统计学习的一些开放问题，这些问题以前没有应用过。以下是我们想要关注的一些问题。

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.