Ensemble subspace, penalty, pretest, and shrinkage strategies for high dimensional data

高维数据的集成子空间、惩罚、预测试和收缩策略

• 批准号: RGPIN-2017-05228
• 负责人: Ahmed, Syed
• 金额: $ 3.13万
• 依托单位: Brock University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758620
• 关键词: Ensemble; subspace; penalty; pretest; shrinkage

There are a host of buzzwords in today's data-centric world. We encounter data in all walks of life, and for analytically- and objectively-minded people, data is crucial to their goals. Making sense of the data and extracting meaningful information from it may not be an easy task. The growth in the size and scope of data sets in a host of disciplines has created a need for innovative statistical strategies for understanding and analyzing such data. A variety of statistical and computational tools are needed to reveal the story that is contained in the data. We define high dimensional data (HDD) as data sets for which the number of predictors are larger than the sample size. The analysis of HDD is an important feature in a host of research fields such as social media, engineering networks, bio-informatics, environmental, and others. The buzzword “Big Data” is nebulously defined, but its problems are real and statisticians play a vital role in this data world. Undoubtedly, overcoming the challenges of HDD is key to successful research in a host of fields. Many organizations are using sophisticated number-crunching, data mining, or Big Data analytics to reveal patterns based on collected information. Clearly, there is an increasing demand for efficient prediction strategies for analyzing HDD. Some examples of HDD that have prompted demand are gene expression arrays, social network modeling, clinical, genetics and phenotypic data.Most of the exiting methods for dealing with HDD begin with model selection for further investigation. Penalized methods are unstable unless very stringent conditions are imposed. This research proposal in HDD focusses on post selection strategies to combat some of the issues inherited in penalized methods. We also propose to investigate ensemble strategy and tuning-parameter free strategy to analyze HDD. Further, I will consider model misspecification problems in HDD and provide a systematic analysis of pretest procedures via divergence theory. Finally, we will develop Bayesian methodology for brain imaging and genetic data. The overarching objective is to provide answers to the question “what are the tools and tricks, pitfalls, applications, challenges and opportunities in HDD analysis”.This proposal emphasizes that statisticians can play a dominant role in solving Big Data problems, and will move statisticians from the cellar of the scientific discovery to the penthouse. The proposed research will provide opportunities for training highly qualified personnel at all levels. The training will be three-fold, methodological, coding/computational, and analysis of data from the real life problems. More public and private sectors are now acknowledging the importance of statistical tools and its critical role in analyzing Big Data. According to a research 4 million jobs may be available globally for Big Data analysis. The proposed research will train individuals for these jobs.

当今以数据为中心的世界中有许多流行语。我们在各行各业都会遇到数据，对于具有分析能力和客观思维的人来说，数据对于他们的目标至关重要。理解数据并从中提取有意义的信息可能不是一件容易的事。许多学科数据集的规模和范围的增长需要创新的统计策略来理解和分析这些数据。需要各种统计和计算工具来揭示数据中包含的故事。我们将高维数据（HDD）定义为预测变量数量大于样本大小的数据集。 HDD 分析是社交媒体、工程网络、生物信息学、环境等众多研究领域的一个重要特征。 “大数据”这个流行词的定义很模糊，但它的问题是真实存在的，统计学家在这个数据世界中发挥着至关重要的作用。毫无疑问，克服 HDD 的挑战是许多领域研究成功的关键。许多组织正在使用复杂的数字处理、数据挖掘或大数据分析来根据收集的信息揭示模式。显然，对分析 HDD 的有效预测策略的需求日益增长。引起需求的 HDD 的一些例子包括基因表达阵列、社交网络建模、临床、遗传学和表型数据。大多数处理 HDD 的现有方法都是从模型选择开始进行进一步研究。除非施加非常严格的条件，否则惩罚方法是不稳定的。 HDD 中的这项研究提案侧重于职位选择策略，以解决惩罚方法中继承的一些问题。我们还建议研究集成策略和无调整参数策略来分析 HDD。此外，我将考虑 HDD 中的模型错误指定问题，并通过发散理论对预测试过程进行系统分析。最后，我们将开发用于脑成像和遗传数据的贝叶斯方法。总体目标是回答“HDD 分析中的工具和技巧、陷阱、应用、挑战和机遇是什么”这一问题。该提案强调统计学家可以在解决大数据问题中发挥主导作用，并将把统计学家从科学发现的地窖搬到顶层公寓。拟议的研究将为培训各级高素质人才提供机会。培训将分为三部分：方法论、编码/计算以及现实生活问题数据的分析。现在，越来越多的公共和私营部门认识到统计工具的重要性及其在分析大数据中的关键作用。根据一项研究，全球可能有 400 万个工作岗位可用于大数据分析。拟议的研究将为这些工作培训个人。