Multivariate Histograms and Inference with Finite Sample Guarantees
具有有限样本保证的多元直方图和推理
基本信息
- 批准号:1916074
- 负责人:
- 金额:$ 25万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2019
- 资助国家:美国
- 起止时间:2019-07-15 至 2023-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Data that comprise several different measurements on each subject are common for modern big data. In order to store these big data in a database as well as for other applications, it is essential to summarize these big data in a compact form without losing important information. This is known to be a difficult problem due to a phenomenon called the `curse of dimensionality'. This research will implement a concrete plan to overcome this stumbling block for a number of important data analysis tasks. Importantly, the resulting methodology will provide relevant guarantees for the accuracy of these analysis tasks as well as fast algorithms for their implementation. The award will provide support of graduate training through research.Density estimation based on multivariate data is known to be a difficult problem due to the `curse of dimensionality'. But in many applications the density is not the final goal of the inference, rather it is a stepping stone to access other objectives. In particular, the histogram represents a summary of the data for the main purpose of showing important features in the data, such as modes, and for estimating probabilities of subsets of the population. This proposal will address the latter problem directly in order to derive a useful multivariate histogram. The research will develop simultaneous confidence bounds with finite sample guarantees for the probability contents of certain data-dependent subsets of the sample space. It will be shown that these bounds possess certain optimality properties and that the widths of the bounds depend essentially only on the probability content of the sets and not on the dimensionality of the space, thus avoiding the curse of dimensionality. The project will develop fast algorithms to construct a histogram that satisfies these bounds and which therefore inherits these properties. The research will investigate the performance of this histogram, also in regards to detecting important features in the distribution such as modes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
对于现代大数据来说,包含每个主题的几个不同度量的数据是常见的。为了将这些大数据存储在数据库中以及用于其他应用程序,必须在不丢失重要信息的情况下以紧凑的形式汇总这些大数据。众所周知,这是一个难题,因为有一种现象称为“维度诅咒”。这项研究将实施一个具体的计划,以克服这一绊脚石,以完成一些重要的数据分析任务。重要的是,由此产生的方法将为这些分析任务的准确性提供相关保证,并为其实施提供快速算法。该奖项将通过研究为研究生培训提供支持。众所周知,由于“维度诅咒”,基于多变量数据的密度估计是一个难题。但在许多应用中,密度并不是推理的最终目标,而是访问其他目标的垫脚石。具体地说,直方图表示数据的汇总,主要目的是显示数据中的重要特征,例如模式,并用于估计总体子集的概率。这一建议将直接解决后一个问题,以便得出有用的多变量直方图。该研究将为样本空间中某些依赖于数据的子集的概率内容开发有限样本保证的同时置信限。结果表明,这些界限具有一定的最优性,而且界限的宽度本质上只取决于集合的概率含量,而不取决于空间的维度,从而避免了维度灾难。该项目将开发快速算法来构建满足这些界限并因此继承这些属性的直方图。这项研究将调查这一直方图的表现,以及在检测分布中的重要特征方面,如模式。这一奖项反映了NSF的法定使命,并通过使用基金会的智力优势和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Guenther Walther其他文献
Guenther Walther的其他文献
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{{ truncateString('Guenther Walther', 18)}}的其他基金
ATD: Statistical methodology and algorithms for detection problems
ATD:检测问题的统计方法和算法
- 批准号:
1220311 - 财政年份:2012
- 资助金额:
$ 25万 - 项目类别:
Continuing Grant
Detection with scan statistics and average likelihood ratio: Methodology
使用扫描统计数据和平均似然比进行检测:方法论
- 批准号:
1007722 - 财政年份:2010
- 资助金额:
$ 25万 - 项目类别:
Continuing Grant
CAREER: Statistics for Flow Cytometry and Freshman Seminars
职业:流式细胞术统计和新生研讨会
- 批准号:
9875598 - 财政年份:1999
- 资助金额:
$ 25万 - 项目类别:
Standard Grant
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