New algorithms for consistent model selection beyond linear models

用于超越线性模型的一致模型选择的新算法

• 批准号: 1607840
• 负责人: Xuming He
• 金额: $ 30万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 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: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1607840&HistoricalAwards=false
• 关键词: New; algorithms; consistent; model; selection

Statistical model building is an important part of scientific discovery. In the big data era, high dimensional data arise frequently. Model selection in the presence of high dimensional features in the framework of linear models, generalized linear models, and models with censored data has been a very active area of research in recent years. The PI aims to develop new algorithms for model selection, within a Bayesian computational framework, that are scalable for high dimensional problems. The PI motivates the proposed research through collaborations with scientists in atmospheric sciences, genetics, and kinesiology, and aims to develop methodologies that are broadly applicable in statistical modeling and data analysis. Much of the recent work has focused on shrinkage through penalization or regularization. Bayesian computational methods, when interpreted broadly, play a valuable role in statistics, including model selection and estimation, but face important hurdles in high dimensional statistics, both in theoretical intricacy and in computational scalability. The PI aims to develop a theoretical framework to demonstrate model selection consistency from the frequentist perspective, which offers interesting insights into why Bayesian model selection methods can provide an asymptotic approximation to the L0 penalty. An important part of the proposed work is the development of a modified Gibbs sampler in the selection of sparse models that is much more scalable than standard MCMC algorithms in the presence of high dimensional variables. The Bayesian methods are especially useful in problems with non-convex objective functions, where Bayesian computation methods can be more robust in performance than direct optimization. A primary application of such a problem considered in the project is quantile regression for censored data. In addition to model selection, the PI proposes a new estimation method for censored quantile regression that promises to be computationally and statistically efficient. Equally importantly, the new method adapts easily to general forms of censoring that other estimation methods have found difficult to handle. The PI will continue integrating research with education by working with PhD students and by providing research experiences for undergraduate students. The research output will be properly disseminated through conferences and workshops and through publication in widely read journals in statistical science.

统计模型的建立是科学发现的重要组成部分。在大数据时代，高维数据频繁出现。 在线性模型、广义线性模型和删失数据模型的框架下，高维特征下的模型选择是近年来一个非常活跃的研究领域。 PI的目的是开发新的算法模型选择，贝叶斯计算框架内，是可扩展的高维问题。 PI通过与大气科学，遗传学和运动学科学家的合作来激励拟议的研究，旨在开发广泛适用于统计建模和数据分析的方法。 最近的大部分工作都集中在通过惩罚或正规化收缩。 贝叶斯计算方法，当广义地解释时，在统计学中起着有价值的作用，包括模型选择和估计，但在高维统计中面临着重要的障碍，无论是在理论上的复杂性和计算的可扩展性。 PI旨在开发一个理论框架，从频率论的角度来证明模型选择的一致性，这为贝叶斯模型选择方法为什么可以提供L0惩罚的渐近近似提供了有趣的见解。所提出的工作的一个重要组成部分是一个修改后的吉布斯采样器的稀疏模型的选择，这是更可扩展的比标准的MCMC算法在高维变量的存在下的发展。贝叶斯方法在具有非凸目标函数的问题中特别有用，其中贝叶斯计算方法在性能上比直接优化更鲁棒。在这个项目中考虑的这样一个问题的主要应用是分位数回归删失数据。除了模型选择之外，PI还提出了一种新的估计方法，用于删失分位数回归，该方法有望在计算和统计上有效。同样重要的是，新方法很容易适应一般形式的审查，其他估计方法已经发现难以处理。PI将通过与博士生合作并为本科生提供研究经验，继续将研究与教育相结合。研究成果将通过会议和讲习班以及在广泛阅读的统计科学期刊上发表的方式适当传播。