Graphical Multi-Resolution Scanning for Cross-Sample Variation

针对跨样本变化的图形多分辨率扫描

• 批准号: 1612889
• 负责人: Li Ma
• 金额: $ 34.51万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1612889&HistoricalAwards=false
• 关键词: Graphical; Multi; Resolution; Scanning; Cross

Identifying variation across data sets is one of the most commonly encountered statistical inferential tasks, and it lies at the heart of numerous applications in a wide range of fields from astrophysics and biology to economics and political science. The recent explosion of "big data" has raised several critical challenges in detecting cross-sample variation, which render existing methods inadequate and entail an urgent need for new methodologies. The most notable and prevalent challenges include complex distributional structures, the highly local nature of variation, various extraneous sources of variation, data sparsity, and massive computational demand. The overarching aim of this research project is to develop a general framework including theory, methods, algorithms, and software for effectively identifying variation in modern big data sets to address these challenges. Specific inference problems to be addressed in this research project include: (i) identifying differences, especially highly local variations, across multiple data sets; (ii) separating intrinsic (i.e., scientifically interesting) cross-sample variation from extraneous variation; (iii) decomposing cross-sample variation into contributions from multiple sources; and (iv) identifying cross-sample variation and variance components in general random objects, including a variety of processes and functional observations. The use of multi-scale inference and Bayesian nonparametric modeling has led to development of a general probabilistic model-based framework for detecting cross-sample variation that integrates two powerful inference tactics -- multi-resolution scanning and graphical modeling. Multi-resolution scanning is the strategy of scanning through the sample space using windows of various sizes, carrying out testing or estimation for the structure of interest -- the cross-sample variation -- on each window. A class of graphical models is then designed to incorporate various dependency structures across scanning windows and data samples, thereby allowing borrowing strength among windows and related samples to achieve high statistical efficiency in identifying cross-sample variation. The project aims to construct a suite of computationally efficient and theoretically justifiable inferential methods and algorithms and to investigate their statistical properties.

识别数据集之间的差异是最常遇到的统计推断任务之一，它是从天体物理学和生物学到经济学和政治学等广泛领域的众多应用的核心。最近“大数据”的爆炸式增长在检测跨样本变异方面提出了几个关键挑战，这使得现有方法不足，迫切需要新的方法。最显著和普遍的挑战包括复杂的分布结构、变化的高度局部性、各种外来的变化来源、数据稀疏性和大量的计算需求。本研究项目的总体目标是开发一个通用框架，包括理论、方法、算法和软件，以有效识别现代大数据集的变化，以应对这些挑战。本研究项目中需要解决的具体推理问题包括：(i)识别多个数据集之间的差异，特别是高度局部的差异；（ii）从外来变异中分离内在的（即科学上有趣的）跨样本变异；（iii）将跨样本变异分解为来自多个来源的贡献；（iv）识别一般随机对象的跨样本变异和方差成分，包括各种过程和功能观察。多尺度推理和贝叶斯非参数建模的使用导致了一种基于一般概率模型的框架的发展，用于检测跨样本变化，该框架集成了两种强大的推理策略——多分辨率扫描和图形建模。多分辨率扫描是一种使用不同大小的窗口扫描样本空间的策略，在每个窗口上对感兴趣的结构（交叉样本变化）进行测试或估计。然后设计了一类图形模型，将扫描窗口和数据样本之间的各种依赖结构结合起来，从而允许窗口和相关样本之间的借用强度，从而在识别跨样本变异方面达到较高的统计效率。该项目旨在构建一套计算效率高、理论上合理的推理方法和算法，并研究其统计特性。

项目成果

A Bayesian hierarchical model for related densities by using Pólya trees

使用 Pólya 树计算相关密度的贝叶斯分层模型

• DOI: 10.1111/rssb.12346
• 发表时间: 2020
• 期刊: Journal of the Royal Statistical Society: Series B (Statistical Methodology
• 作者: Christensen, Jonathan;Ma, Li
• 通讯作者: Ma, Li

Bayesian Graphical Compositional Regression for Microbiome Data

• DOI: 10.1080/01621459.2019.1647212
• 发表时间: 2019-08-26
• 期刊: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• 影响因子: 3.7
• 作者: Mao, Jialiang;Chen, Yuhan;Ma, Li
• 通讯作者: Ma, Li