Statistical theory on finite alphabet structures: inference, algorithms, and applications
Statistical theory on finite alphabet structures: inference, algorithms, and applications
批准号:
411042450
负责人:
Dr. Merle Behr
金额:
$0.0万
依托单位:
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
项目状态:
已结题
起止时间:
2017-12-31 至 2019-12-31
中文摘要
点击翻译按钮获取中文摘要
英文摘要
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.
期刊论文(2)
专著(0)
科研奖励(0)
会议论文
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
DOI:
10.1038/s43588-021-00056-5
发表时间:
2021-04-01
期刊:
NATURE COMPUTATIONAL SCIENCE
影响因子:
--
作者:
[Pelizzola, Marta, Behr, Merle, Futschik, Andreas]
通讯作者:
Futschik, Andreas
国内基金
海外基金
登录
查看更多内容
Research on Quantum Field Theory without a Lagrangian Description
-
批准号:24ZR1403900
-
项目类别:省市级项目
-
资助金额:--
-
批准年份:2024
-
负责人:SATOSHI NAWATA
-
依托单位:
Fibered纽结的自同胚、Floer同调与4维亏格
-
批准号:12301086
-
项目类别:青年科学基金项目
-
资助金额:30.00万元
-
批准年份:2023
-
负责人:何东泰
-
依托单位:
基于密度泛函理论金原子簇放射性药物设计、制备及其在肺癌诊疗中的应用研究
-
批准号:82371997
-
项目类别:面上项目
-
资助金额:48.00万元
-
批准年份:2023
-
负责人:张春富
-
依托单位:
基于isomorph theory研究尘埃等离子体物理量的微观动力学机制
-
批准号:12247163
-
项目类别:专项项目
-
资助金额:18.00万元
-
批准年份:2022
-
负责人:黄栋
-
依托单位:
Toward a general theory of intermittent aeolian and fluvial nonsuspended sediment transport
-
批准号:--
-
项目类别:--
-
资助金额:55万元
-
批准年份:2022
-
负责人:Thomas Pahtz
-
依托单位:
英文专著《FRACTIONAL INTEGRALS AND DERIVATIVES: Theory and Applications》的翻译
-
批准号:12126512
-
项目类别:数学天元基金项目
-
资助金额:12.0万元
-
批准年份:2021
-
负责人:李常品
-
依托单位:
钱江潮汐影响下越江盾构开挖面动态泥膜形成机理及压力控制技术研究
-
批准号:LY21E080004
-
项目类别:省市级项目
-
资助金额:--
-
批准年份:2020
-
负责人:尹鑫晟
-
依托单位:
基于Restriction-Centered Theory的自然语言模糊语义理论研究及应用
-
批准号:61671064
-
项目类别:面上项目
-
资助金额:65.0万元
-
批准年份:2016
-
负责人:史树敏
-
依托单位:
高阶微分方程的周期解及多重性
-
批准号:11501240
-
项目类别:青年科学基金项目
-
资助金额:18.0万元
-
批准年份:2015
-
负责人:梁树青
-
依托单位:
四维流形上的有限群作用与奇异光滑结构
-
批准号:11301334
-
项目类别:青年科学基金项目
-
资助金额:22.0万元
-
批准年份:2013
-
负责人:李红霞
-
依托单位: