High-dimensional Data Analysis: Modeling Unobserved Heterogeneity in Data, and Studying Imbalanced Classification Problems

高维数据分析：对数据中未观察到的异质性进行建模，并研究不平衡分类问题

• 批准号: RGPIN-2020-05011
• 负责人: Khalili, Abbas
• 金额: $ 1.75万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740345
• 关键词: dimensional; Data; Analysis; Modeling; Unobserved

Data science has become the center of attention in a wide range of scientific disciplines, thanks to ever-expanding means of data collection in today's world. Unprecedented size and structural complexity of current data in many applications call for computationally efficient and statistically sound methodologies for extracting useful information from such data. Toward this goal, the general theme of my research program focuses on analyzing high-dimensional data. More specifically, over the five years of this proposal, my short-term objectives are: I) Statistical modeling of heterogeneous high-dimensional data: In applications such as health sciences, engineering and environment, social sciences, and financial econometrics, high-dimensional data often arise from heterogeneous populations consisting of multiple hidden homogeneous sub-populations. Finite mixture of regressions (FMR) and Markov regime-switching autoregressive (MSAR) models provide flexible tools for capturing unobserved heterogeneity in data. The later models are used for modeling time series data. In practice, when fitting such models to a dataset, one faces three inferential problems: order selection or estimation of the number of hidden sub-populations or regimes, variable selection, and so-called post-selection statistical inference such as hypothesis testing or confidence intervals for parameters of a data-driven selected model. Despite their wide applications, rigorous methodological developments addressing the aforementioned problems in the growing literature on high-dimensional statistics have been very limited. In my short-term objectives, I will investigate new likelihood-based regularization techniques for: order selection in FMR and MSAR, and variable selection in sparse dynamic FMR and vector MSAR with fixed order and in high-dimensional settings. Establishment of such results will pave the way toward post-selection inference problems which are the subjects of my long-term objectives. II) High-dimensional imbalanced classification problems: In applications such as fraud detection, medical diagnosis, or equipment malfunction detection, classification tasks often suffer from both high-dimensionality and imbalance in the observed frequency of some classes in the training data. The latter is due to either data collection process or because some classes are indeed rare in the population. Due to data scarcity in minority class(es), conventional discriminative methods are often biased toward the majority class(es) resulting in much higher misclassification rates for the minority class(es). Imbalanced classification problems are generally hard, so I begin by studying imbalanced linear binary cases. I will investigate the utility of divide-and-conquer techniques coupled with hard-thresholding variable selection methods for bias correction in the standard linear discriminant analysis toward the minority class in high-dimensions. I will also study multi-class problems.

数据科学已成为广泛的科学学科的关注中心，感谢您在当今世界中不断扩展的数据收集手段。在许多应用程序中，当前数据的空前大小和结构复杂性要求从这些数据中提取有用信息的计算高效和统计上的合理方法。为了实现这一目标，我的研究计划的一般主题集中在分析的高维数据上。更具体地说，在该提案的五年中，我的短期目标是：i）非均质高维数据的统计建模：在诸如健康科学，工程和环境，社会科学和金融经济学等应用中，通常是由高维数据引起的，通常是由由多个隐藏同质同质副群组成的异质种群引起的。回归（FMR）和马尔可夫制度转换自回归（MSAR）模型的有限混合物为捕获数据中未观察到的异质性提供了灵活的工具。后来的型号用于建模时间序列数据。实际上，当将此类模型拟合到数据集时，一个人会面临三个推论问题：订单选择或估计隐藏的子人群或制度的数量，可变选择以及所谓的选择后统计推断，例如假设测试或置信区间，例如数据驱动的数据驱动的模型的参数。尽管应用了广泛的应用，但严格的方法论发展解决了不断增长的有关高维统计文献中与理性有关的问题的问题非常有限。在我的短期目标中，我将研究以下新的基于可能性的调节技术：FMR和MSAR中的订单选择，以及具有固定顺序和高维设置的稀疏动态FMR和Vector MSAR中的可变选择。建立此类结果将为选择后推理问题铺平道路，这是我长期目标的主题。 ii）高维不平衡分类问题：在诸如欺诈检测，医学诊断或设备故障检测等应用中，分类任务通常在培训数据中某些类别的某些类别的频率中遭受高差异性和不平衡性。后者是由于数据收集过程，或者是因为某些班级在人群中确实很少见。由于少数民族类别中的数据稀缺性，常规判别方法通常会偏向多数级别（ES），从而导致少数族裔类别（ES）的错误分类率更高。分类问题通常很困难，因此我首先研究了不平衡的线性二元病例。我将调查分界线和互动技术的实用性，并在标准的线性判别分析中对高维度中的少数群体类别中的偏置校正方法进行偏置校正的努力。我还将研究多级问题。