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FORGING: Fortuitous Geometries and Compressive Learning

锻造：偶然几何形状和压缩学习

基本信息

批准号：
EP/P004245/1
负责人：
Ata Kaban
金额：
$ 111.73万
依托单位：
University of Birmingham
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2017
资助国家：
英国
起止时间：
2017 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FP004245%2F1
关键词：
FORGING Fortuitous Geometries Compressive Learning

项目摘要

Statistical machine learning has been instrumental in providing algorithms that enable us to draw valid conclusions from empirical data. Its successes rely crucially on a rigorous mathematical theory. Unfortunately, as the modern data sets are increasingly high dimensional, new challenges gathered under the term `curse of dimensionality' render many of the existing data analysis methods inadequate, questionable, or inefficient, and much of the existing theory becomes uninformative. Mitigating the curse of dimensionality receives a lot of research attention currently. However, many fundamental questions remain unresolved. The aim of this project is to provide answers to two of these:Q1: What kinds of data distributions make a given high dimensional learning problem easier or harder to be solved?Q2: What kinds of learning problems can be approximately solved compressively, on a low dimensional subspace?We propose a stance complementary to efforts that look for ways to counter the various observed detrimental effects of the dimensionality curse: We shall exploit some very generic properties of high dimensional probability spaces to develop a unified theory, and its algorithmic implications, to unearth some precise conditions that enable us to solve high dimensional problems in low dimensions. These conditions will depend on the geometry of the problem. We will use a new notion of problem-dependent compressive distortion that we have started developing, and which will build on a so far unexploited connection between random projections and empirical process theory. The expected outcome will be applicable across a range of different machine learning and data mining problems, and we validate this in case studies.

统计机器学习一直有助于提供算法，使我们能够从经验数据中得出有效的结论。它的成功主要依赖于严格的数学理论。不幸的是，随着现代数据集越来越高维，在“维度灾难”一词下收集的新挑战使得许多现有的数据分析方法不充分，有问题或效率低下，并且许多现有的理论变得缺乏信息。减轻维数灾难是当前研究的热点。然而，许多根本问题仍未解决。这个项目的目的是提供其中两个问题的答案：Q1：什么样的数据分布使给定的高维学习问题更容易或更难解决？Q2：什么样的学习问题可以在低维子空间上近似压缩解决？我们提出了一个补充的努力，寻找方法来对抗各种观察到的维数灾难的不利影响：我们将利用高维概率空间的一些非常通用的属性来发展一个统一的理论，及其算法的影响，挖掘一些精确的条件，使我们能够解决高维问题在低维。这些条件将取决于问题的几何形状。我们将使用我们已经开始发展的问题依赖压缩失真的新概念，它将建立在随机预测和经验过程理论之间迄今尚未开发的联系之上。预期的结果将适用于一系列不同的机器学习和数据挖掘问题，我们在案例研究中验证了这一点。