Bayesian Recursive Partitioning and Inference on the Structure of High-Dimensional Distributions

高维分布结构的贝叶斯递归划分和推理

• 批准号: 1309057
• 负责人: Li Ma
• 金额: $ 15.99万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1309057&HistoricalAwards=false
• 关键词: Bayesian; Recursive; Partitioning; Inference; Structure

This research concerns one of the most important and pervasive classes of problems in modern data analysis---inference on the structure of probability distributions. Specific inference problems to be addressed fall into two broad categories. The first involves inference on the structure of a single probability distribution, including estimation of joint and conditional densities, variable selection in linear regression, and the testing of independence and conditional independence among variables. The second involves inference on the relationship across multiple distributions. This includes testing whether two (or more) data samples have the same underlying distribution, and learning the structure of their difference, with particular interest given to finding local structures---differences that lie in small subsets---in large high-dimensional spaces. To address these problems, the investigator puts forward a novel framework for constructing Bayesian priors on multivariate distributions through recursive partitioning. Inference using this framework is flexible and adaptive. Moreover, the generative nature of these priors facilitates the modeling of dependence structure across multiple distributions and this leads to powerful methods for comparing distributions. To address the computational challenges in high-dimensional problems, the investigator lays out a set of computational strategies and proposes to develop several algorithms that can drastically improve the efficiency of Bayesian posterior inference in high-dimensional problems. These strategies utilize the recursive nature of the proposed framework to efficiently explore the global landscape of the corresponding posterior distributions.Inference on the structure of probability distributions lies at the heart of many scientific inquiries, and new statistical theory and methods are urgently needed to accommodate the ever increasing dimensionality of data sets that is commonplace in modern scientific investigations. Two specific applications that motivate this project are the analysis of high-dimensional flow cytometry data in systems biology for unraveling the functional relationships among proteins as well as the mapping of human genes to various qualitative and quantitative traits, in particular those of common diseases such as cancer and diabetes. The concepts, theory, methodology, and algorithms developed in this project will be directly applicable to these problems, as well as to the analysis of data sets arising from a wide variety of other fields ranging from environmental science to economics.

本研究涉及现代数据分析中最重要和最普遍的一类问题——概率分布结构的推断。要解决的具体推理问题分为两大类。第一部分涉及对单个概率分布结构的推断，包括联合密度和条件密度的估计，线性回归中的变量选择，以及变量之间独立性和条件独立性的检验。第二种方法涉及对多个分布之间关系的推断。这包括测试两个（或更多）数据样本是否具有相同的底层分布，并学习它们之间差异的结构，特别关注在大的高维空间中寻找局部结构——位于小子集中的差异。为了解决这些问题，研究者提出了一种新的框架，通过递归划分在多变量分布上构造贝叶斯先验。使用该框架的推理是灵活和自适应的。此外，这些先验的生成性质有助于跨多个分布建立依赖结构的建模，这导致了比较分布的强大方法。为了解决高维问题中的计算挑战，研究者提出了一套计算策略，并建议开发几种算法，这些算法可以大大提高贝叶斯后验推理在高维问题中的效率。这些策略利用所提出框架的递归性质来有效地探索相应后验分布的全局景观。对概率分布结构的推断是许多科学研究的核心，迫切需要新的统计理论和方法来适应现代科学研究中日益增加的数据集维数。激发这个项目的两个具体应用是分析系统生物学中的高维流式细胞术数据，以揭示蛋白质之间的功能关系，以及人类基因与各种定性和定量特征的映射，特别是癌症和糖尿病等常见疾病。在这个项目中开发的概念、理论、方法和算法将直接适用于这些问题，以及从环境科学到经济学等各种其他领域产生的数据集的分析。