RUI: Fourier Methods in Machine Learning Theory and Practice

CCR-9877079 Jackson迄今为止，从机器学习的理论研究中获得的一些最强有力的结果使用了离散傅立叶分析的方法。 该项目旨在进一步应用这些方法来回答重要的开放式理论机器学习问题，并开发几个傅立叶结果的实际应用。 具体而言，计划开展三项工作。 (1)扩展PI先前NSF资助的项目下获得的结果，以进一步改善许多傅立叶基算法的关键组件的渐近运行时间。(2)将傅立叶技术应用于几个有趣的开放问题，特别是那些关于从被各种噪声过程破坏的数据中学习的实际启发问题。(3)实施和经验评估各种基于傅立叶的算法，包括作为前两个任务的一部分开发的算法以及其他算法。 考虑的应用包括从人工神经网络和修剪决策树中提取规则。 除了我们对机器学习知识的预期进步外，该项目还将为一个本科院校的一名或多名本科生的研究培训做出重大贡献。

CCR-9877079JacksonSome of the strongest results obtained to date from the theoretical study of machine learning have used methods from discrete Fourier analysis. This project seeks both to further apply these methods to answer significant open theoretical machine learning questions and to develop practical applications of several Fourier results. Specifically, three tasks are planned. (1) Extend results obtained under the PI's prior NSF-funded project to further improve the asymptotic run time of a key component of many Fourier-base algorithms. (2) Apply Fourier techniques to several interesting open problems, particularly those concerning the practically inspired problem of learning form data corrupted by various noise processes. (3) Implement and empirically evaluate a variety of Fourier-based algorithms, including those developed as part of the first two tasks, as well as others. Applications considered include extracting rules from artificial neural networks and pruning decision trees. In addition to anticipated advancements in our knowledge about machine learning, this project will contribute substantially to the research training of one or more undergraduate students at a largely undergraduate institution.