Bayesian Partition Models for Detecting Influential and Interactive Variables

回归建模中的变量选择是统计学中一个长期存在的问题。最近，由于数据收集技术的巨大进步，如生物学、互联网和市场营销领域的数据收集技术，人们对分析优雅、数字健壮和算法高效的变量选择方法产生了极大的兴趣。本文考虑了具有离散协变量的单变量和多变量高维回归问题中的模型选择问题。主要目标是发展贝叶斯方法，以便发现影响反应的某些独立变量（例如，遗传标记）之间的相互作用。通过采用朴素贝叶斯建模的观点，并引入灵活的潜在结构来建模变量之间的依赖关系，研究者将设计方法，可以检测成千上万个候选预测因子中少数协变量的相互作用。通过介绍？个人类型?变量，研究者概述了一种策略，将协变量的建模与响应的建模解耦。该策略允许将协变量的子集与响应的子集联系起来，这是许多生物医学研究的重要目标。将这些思想扩展到具有连续协变量的情况的策略将被探索和测试。这项研究还将把这些新方法和理论的力量带到遗传学、生物信息学和经济数据分析等几个重要的应用领域。从大量候选预测因子中选择一个子集来准确预测某些结果（例如天气、股票价格运动、心脏病风险等）是统计学中一个长期存在且具有挑战性的问题。最近，由于数据收集技术的巨大进步，如生物学、互联网和市场营销领域的数据收集技术，人们对分析优雅、数字健壮和算法高效的变量选择方法产生了极大的兴趣。现在，普通科学家和定量建模者都广泛认识到，在众多候选因素中发现对结果/反应真正有影响的因素的重要性。提出的研究是由重要的遗传学和基因组学问题的动机。其目标是开发统计和计算策略，不仅选择信息预测因子，而且发现预测因子之间可能显著影响结果的相互作用。在遗传学中，这种基因突变之间的相互作用被称为上位性。它们的检测是后基因组时代的主要挑战之一。在艾滋病毒耐药性突变研究中，这种相互作用往往揭示了病毒耐药性分子基础的新见解，并可能导致创新和有效的治疗方法。期望它既丰富统计建模理论，又提供适用于不同领域的广泛问题的新颖计算和统计策略。研究者开发的初步工具已经成功地应用于许多遗传学和生物医学研究。这些方法也可以很容易地适用于许多？数据挖掘”?任务，如文本挖掘、网络研究和电子商务。它将为研究生提供教育和跨学科的研究机会，并将产生生物医学研究人员、经济学家和其他实践者可能感兴趣的软件。

Variable selection in regression modeling is a long-standing problem in statistics. Recently, there has been a significant surge of interest in analytically elegant, numerically robust, and algorithmically efficient variable selection methods, largely due to the tremendous advance in data collection techniques such as those in biology, internet, and marketing. This proposal considers the model selection problem in both univariate and multivariate high-dimensional regression problems with discrete covariates. The main goal is to develop Bayesian methodologies enabling the discovery of interactions among certain independent variables (e.g., genetic markers) affecting the response(s). By taking a Naive Bayes modeling perspective and introducing flexible latent structures to model dependence among variables, the investigator will design methods that can detect interactions of a handful of covariates among tens of thousands of candidate predictors. By introducing ?individual type? variables, the investigator outlines a strategy to decouple the modeling of the covariates from that of the responses. This strategy allows one to link a subset of covariates to a subset of the responses, which is an important goal in many biomedical studies. Strategies for extending the ideas to cases with continuous covariates will be explored and tested. This research will also bring the power of these new methods and theory to bear on several important application areas such as genetics, bioinformatics, and economic data analysis.Selecting a subset of predictors among a large number of candidates for accurate prediction of certain outcomes (e.g., weather, stock price movement, heart disease risk etc) is a long-standing and challenging problem in statistics. Recently, there has been a significant surge of interest in analytically elegant, numerically robust, and algorithmically efficient variable selection methods, largely due to the tremendous advance in data collection techniques such as those in biology, internet, and marketing. It has now been widely recognized by both general scientists and quantitative modelers the importance of discovering among many candidate factors that are truly influential on the outcomes/responses. The proposed research is motivated by important genetics and genomics problems. Its goal is to develop statistical and computational strategies for not only selecting informative predictors but also discovering interactions among the predictors that may significantly influence the outcome. In genetics, such interactions among genetic mutations are called ?epistasis,? and their detection is one of the main challenges in the post-genome era. In HIV drug-resistance mutation studies, such interactions often reveal new insights on the molecular basis of virus's drug resistance and can lead to innovative and effective treatments. It is expected both to enrich statistical modeling theory and to provide novel computational and statistical strategies applicable to a wide range of problems in diverse fields. The preliminary tools the investigator has developed have already been successfully applied to a number of genetics and biomedical studies. These methods can also be readily applicable to many ?data mining'? tasks, such as text mining, network studies, and e-commerce. It will provide both educational and interdisciplinary research opportunities for graduate students, and will result in software that may be of interest to biomedical researchers, economists, and other practitioners.