Distances in Robust Model Selection

鲁棒模型选择中的距离

• 批准号: 0504957
• 负责人: Marianthi Markatou
• 金额: --
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504957&HistoricalAwards=false
• 关键词: Distances; Robust; Model; Selection

Clean data is prerequisite for most statistical analyses. An ideal solution, when questionable data items arise, is to go back to check the source. However, in many cases this is not possible. Contamination therefore is an important problem, and robust techniques that can handle large data sets are needed to cope with this problem. The role of distances in the problem of robust model selection is examined. It is argued that robust model assessment and selection is an important problem that has not received adequate attention in the literature. It is suggested that distances offer potentially valuable tools for addressing various aspects of the problem of modeling, one of which is the aspect of robustness. A new framework is proposed that differs from the classical robustness paradigm in at least two aspects. Most of the developments in classical robustness center around location-scale models and the concepts therefrom. Attempts to extend classical robust procedures to other non location-scale models were met with limited success. The methodology proposed here incorporates easily a wide variety of models, including location-scale models. The starting point of the new proposal is the identification of a goodness-of-fit measure that provides an assessment of whether a given model approximates the mechanism that generated the data. It is then examined in what sense the measure is robust. Distances have been used extensively in many scientific fields such as genetics, physics, sociology, anthropology and more recently in the field of machine learning. The significance of this work is two-fold. Within the scientific field of statistics, a very general framework, that can address the problem of robust model assessment and selection is offered, that can handle large data sets and allows to measure the extend to which the model approximates the phenomenon under study. Outside the field of statistics the technology and scientific results can be extended and applied to address important problems in clinical informatics and bioequivalence.

干净的数据是大多数统计分析的先决条件。当出现可疑数据项时，一个理想的解决方案是返回检查源。然而，在许多情况下，这是不可能的。因此，污染是一个重要的问题，并且需要能够处理大数据集的鲁棒技术来科普这个问题。研究了距离在鲁棒模型选择问题中的作用。有人认为，鲁棒模型的评估和选择是一个重要的问题，在文献中没有得到足够的重视。有人建议，距离提供了潜在的有价值的工具，用于解决建模问题的各个方面，其中之一是鲁棒性方面。提出了一个新的框架，不同于经典的鲁棒性范式在至少两个方面。经典鲁棒性的大部分发展都围绕着位置-尺度模型及其概念。试图将经典的稳健程序扩展到其他非位置-尺度模型，但成功有限。这里提出的方法很容易结合了各种各样的模型，包括位置规模模型。新提案的出发点是确定一个拟合优度衡量标准，以评估给定模型是否接近产生数据的机制。然后检查在什么意义上该措施是稳健的。 距离在许多科学领域中得到了广泛的应用，如遗传学、物理学、社会学、人类学，最近还被用于机器学习领域。这项工作的意义是双重的。在统计学的科学领域内，提供了一个非常通用的框架，可以解决稳健模型评估和选择的问题，可以处理大型数据集，并允许测量模型近似研究中现象的程度。在统计学领域之外，技术和科学成果可以扩展并应用于解决临床信息学和生物等效性方面的重要问题。