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Statistical theory on finite alphabet structures: inference, algorithms, and applications

有限字母表结构的统计理论：推理、算法和应用

基本信息

批准号：
411042450
负责人：
Dr. Merle Behr
金额：
--
依托单位：
Department of Statistics
依托单位国家：
德国
项目类别：
Research Fellowships
财政年份：
2018
资助国家：
德国
起止时间：
2017-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/411042450?language=en
关键词：
Statistical theory finite alphabet structures

项目摘要

A vast amount of research of modern statistics is concerned with problems that are highly underdetermined, in the sense that the amount of unknown parameters is (much) larger than the amount of observable data. This renders estimation of and inference about such parameters impossible per se, as the parameters are not identifiable. Therefore, it is pertinent to include additional structural information. In a broader sense, this is achieved by some kind of sparsity: although the parameter of interest is complex (e.g., high-dimensional), it has a simple (e.g., low-dimensional) underlying structure. The focus of this proposal is on a type of sparsity that has received relatively few attention so far, namely, sparsity in the function values of a signal via a given finite alphabet (FA). FA structures appear in many different fields, for example, in cancer genetics, where DNA copy-numbers can only take one of a few known integer values, and in digital communications with binary signals.In the theoretical part of this project, we want to analyze, jointly with Prof. Martin Wainwright (UC Berkeley) and Prof. Bin Yu (UC Berkeley), how FA structures can enable meaningful inference in underdetermined statistical models, in place of and in combination with classical sparsity. Thereby, we want to focus on blind source separation and high-dimensional linear models. Although, FA structures solve the problem of non-identifiability, their combinatorial nature leads to a computational burden. Therefore, a fundamental research objective of this proposal is to precisely quantify this gap between statistical minimax optimality and computational feasibility. In particular, we want to develop fast algorithms, which, at the same time, yield adequate statical efficiency.On this basis, in the analytical part of this project, we want to consider a modification of FA structures: Subgroup detection for clinical trials often leads to segmentation problems, where a specific FA is induced by phylogenetic trees. We want to tackle those problems with multiscale procedures. Those do not just provide minimax optimal estimates, but also confidence statements, something which can be particularly crucial in medical applications. In cooperation with Prof. Bin Yu (UC Berkeley) and the Wellcome Trust Center for Human Genetics (Oxford) we want to demonstrate with real data examples how FA-procedures provide significant improvement in personalized medicine.

现代统计学的大量研究都涉及高度欠定的问题，即未知参数的数量（远）大于可观察数据的数量。这使得对这些参数的估计和推断本身是不可能的，因为这些参数是不可识别的。因此，有必要包括额外的结构信息。在更广泛的意义上，这是通过某种稀疏性来实现的：尽管感兴趣的参数是复杂的（例如，高维），它具有简单的（例如，低维）底层结构。这个建议的重点是一种类型的稀疏性，迄今为止，已收到相对较少的关注，即，稀疏性的信号通过一个给定的有限字母表（FA）的函数值。FA结构出现在许多不同的领域，例如，在癌症遗传学中，DNA拷贝数只能取少数已知整数值中的一个，以及在二进制信号的数字通信中，在这个项目的理论部分，我们想与Martin温赖特教授一起分析（加州大学伯克利分校）和教授于斌（加州大学伯克利分校），FA结构如何在欠定统计模型中实现有意义的推断，代替经典稀疏性并与之结合。因此，我们希望专注于盲源分离和高维线性模型。虽然FA结构解决了不可识别性的问题，但其组合性质导致计算负担。因此，这个建议的一个基本研究目标是精确地量化统计极大极小最优性和计算可行性之间的差距。特别是，我们要开发快速算法，其中，在同一时间，产生足够的静态efficiency.On在此基础上，在本项目的分析部分，我们要考虑修改FA结构：亚组检测临床试验往往会导致分割问题，其中一个特定的FA是由系统发育树诱导。我们希望用多尺度程序来解决这些问题。这些不仅提供了最小最大最优估计，而且还提供了置信度声明，这在医学应用中尤为重要。在与Bin Yu教授（加州大学伯克利分校）和Wellcome人类遗传学信托中心（牛津大学）的合作中，我们希望用真实的数据例子来证明FA程序如何在个性化医疗中提供显着的改进。

项目成果

期刊论文数量（2）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Testing for dependence on tree structures

DOI：
10.1073/pnas.1912957117
发表时间：
2020-05-05
期刊：
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
影响因子：
11.1
作者：
Behr, Merle;Ansari, M. Azim;Holmes, Chris
通讯作者：
Holmes, Chris

Multiple haplotype reconstruction from allele frequency data