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, Ejaz
• 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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=711341
• 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.

在当今以数据为中心的世界里，有许多流行语。我们在各行各业都会遇到数据，对于分析和客观的人来说，数据对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。许多学科中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包含在数据中的故事。我们将高维数据（HDD）定义为预测因子数量大于样本量的数据集。硬盘分析是许多研究领域的重要特征，如社会媒体、工程网络、生物信息学、环境等。“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扮演着至关重要的角色。毫无疑问，克服HDD的挑战是在许多领域成功研究的关键。许多组织正在使用复杂的数字运算、数据挖掘或大数据分析来揭示基于收集信息的模式。显然，对于分析HDD的有效预测策略的需求正在增加。推动需求的硬盘的一些例子是基因表达阵列、社会网络建模、临床、遗传学和表型数据。