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

在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，对于具有分析和客观思维的人来说，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情。许多学科数据集的规模和范围的增长，产生了对理解和分析这些数据的创新统计战略的需求。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）定义为预测因子数量大于样本大小的数据集。HDD的分析是诸如社交媒体、工程网络、生物信息学、环境等许多研究领域的重要特征。“大数据”这个流行词定义模糊，但它的问题是真实的，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的信息的模式。显然，对用于分析HDD的有效预测策略的需求日益增加。HDD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。现有的大多数处理HDD的方法开始都是从模型选择开始的，以进行进一步的研究。惩罚方法是不稳定的，除非施加非常严格的条件。HDD的这项研究建议侧重于职位选择策略，以解决惩罚方法中继承的一些问题。我们还提出了研究集成策略和调谐参数自由策略来分析HDD。此外，我将考虑模型误指定问题，在HDD和提供一个系统的分析，通过发散理论的预测试程序。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方面发挥主导作用，并将统计学家从科学发现的地窖转移到顶层公寓。拟议的研究将为培训各级高素质人员提供机会。培训将是三重的，方法，编码/计算，并从真实的生活问题的数据分析。越来越多的公共和私营部门现在认识到统计工具的重要性及其在分析大数据方面的关键作用。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。这项研究将为这些工作培训个人。*

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.******