Collaborative Research: Bayesian and Semi-Bayesian Methods for Detecting Relationships in High Dimensions

合作研究：用于检测高维关系的贝叶斯和半贝叶斯方法

• 批准号: 2015411
• 负责人: Jun Liu
• 金额: $ 12万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-15 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2015411&HistoricalAwards=false
• 关键词: Collaborative; Research; Bayesian; Semi; Methods

In this big-data era, massive data sets are being generated routinely and we are seeing a growing need for powerful, reliable, and interpretable statistical learning tools to help understand these data. The main ideas and approaches in this projectl focus on developing effective statistical learning tools to learn about complex and heterogeneous structures, such as those changing in time or varying among different groups of individuals, in high-dimensions. The activities will have a significant impact on high dimensional Bayesian analysis and modeling of nonlinear relationships. While most current efforts for high-dimensional Bayesian analyses have been focused on linear models, this project focuses on two ways of generalizing standard linear models to meet certain practical challenges: one is a generalized form of mixture modeling, termed as individualized variable selection, which enables each individual observation to have its own set of dependent variables through the employment of neuronized priors. Another extension is the Bayesian inference of index models that form a mixture structure. The project will lead to useful tools (or customized software) for discovering interpretable nonlinear and interactive patterns among a large number of potential variables. Various aspects of statistical modeling, design, and learning strategies integrated in our algorithms are broadly applicable to problems involving signal discovery in complex systems and high-dimensional data. The project will also provide both educational and interdisciplinary research opportunities for graduate students, and will result in software useful to biomedical researchers, economists, social scientists, and many other practitioners. In a vast number of regression problems, especially under high-dimensional settings, the structure of the association between covariates in hand and the target quantity of interest might be heterogeneous over observations, which calls for effective methods to detect such non-trivial structures. Standard procedures, including traditional variable selections, commonly overlook the existence of interplays of these heterogeneous factors. This research project aims to develop statistical procedures that identify the complicated relationship between response Y and a set of covariates X in flexible and computationally efficient ways. Project 1 focuses on Bayesian individualized variable selection (BIVS), which generalizes standard linear regression models to quantify heterogeneous effects among individual observations that differ in their dependent variables with different magnitudes. The PIs will investigate its theoretical properties, including model selection consistency and its robustness when the model assumption is violated. Project 2 is devoted to the development of an efficient Bayesian method to infer the semi-parametric relationship between the response and covariates through general index models. The PIs will explore its computational feasibility and theoretical properties such as the posterior contraction rate on the estimation of the sufficient dimension reduction space. Project 3 focuses on a fast tuning parameter selection procedure by employing a generative process via neural networks. By using this procedure, the cross-validation can be efficiently implemented for general models, such as the BIVS and Bayesian index models, regularized variable selection, and nonparametric function estimation.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.

在这个大数据时代，大量的数据集正在常规地生成，我们越来越需要强大、可靠、可解释的统计学习工具来帮助理解这些数据。本项目的主要思想和方法侧重于开发有效的统计学习工具，以了解复杂和异质结构，例如那些随时间变化或在不同个体群体之间变化的高维结构。这些活动将对高维贝叶斯分析和非线性关系建模产生重大影响。虽然目前大多数高维贝叶斯分析的努力都集中在线性模型上，但本项目侧重于两种推广标准线性模型的方法，以应对某些实际挑战：一种是广义形式的混合建模，称为个性化变量选择，它使每个单独的观察都有自己的一组因变量，通过使用神经元化先验。另一个扩展是形成混合结构的索引模型的贝叶斯推理。该项目将产生有用的工具（或定制软件），用于在大量潜在变量中发现可解释的非线性和交互模式。统计建模、设计和学习策略的各个方面集成在我们的算法中，广泛适用于复杂系统和高维数据中的信号发现问题。该项目还将为研究生提供教育和跨学科的研究机会，并将产生对生物医学研究人员、经济学家、社会科学家和许多其他实践者有用的软件。在大量的回归问题中，特别是在高维设置下，在手中的协变量和感兴趣的目标数量之间的关联结构可能在观察中是异质的，这需要有效的方法来检测这种非平凡结构。标准程序，包括传统的变量选择，通常忽略了这些异质因素之间相互作用的存在。本研究项目旨在开发统计程序，以灵活和计算高效的方式识别响应Y和一组协变量X之间的复杂关系。项目1的重点是贝叶斯个性化变量选择（BIVS），它推广了标准线性回归模型，以量化不同程度因变量不同的个体观测值之间的异质性效应。pi将研究其理论性质，包括模型选择一致性和模型假设违反时的鲁棒性。项目2致力于开发一种有效的贝叶斯方法，通过一般指数模型来推断响应与协变量之间的半参数关系。pi将探讨其计算可行性和理论性质，如对足够降维空间估计的后验收缩率。项目3侧重于通过神经网络采用生成过程的快速调谐参数选择程序。利用该方法，可以有效地实现一般模型的交叉验证，如BIVS和贝叶斯指数模型、正则化变量选择和非参数函数估计。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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

False Discovery Rate Control via Data Splitting

• DOI: 10.1080/01621459.2022.2060113
• 发表时间: 2022-05-25
• 期刊: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• 影响因子: 3.7
• 作者: Dai, Chenguang;Lin, Buyu;Liu, Jun S.
• 通讯作者: Liu, Jun S.

Neuronized Priors for Bayesian Sparse Linear Regression

• DOI: 10.1080/01621459.2021.1876710
• 发表时间: 2018-09
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Minsuk Shin;Jun S. Liu

Varying Coefficient Model via Adaptive Spline Fitting

通过自适应样条拟合改变系数模型

• DOI: 10.1080/10618600.2023.2267616
• 发表时间: 2023
• 期刊: Journal of Computational and Graphical Statistics
• 影响因子: 2.4
• 作者: Wang, Xufei;Jiang, Bo;Liu, Jun S.
• 通讯作者: Liu, Jun S.

Bayesian bi-clustering methods with applications in computational biology

• DOI: 10.1214/22-aoas1622
• 发表时间: 2020-07
• 期刊: The Annals of Applied Statistics
• 作者: Han Yan;Jiexing Wu;Y. Li;Jun S. Liu

Stratification and Optimal Resampling for Sequential Monte Carlo

顺序蒙特卡罗的分层和最佳重采样

• DOI: 10.1093/biomet/asab004
• 发表时间: 2020-04
• 期刊: Biometrika
• 影响因子: 2.7
• 作者: Yichao Li;Wenshuo Wang;Ke Deng;Jun S. Liu
• 通讯作者: Jun S. Liu