Fractional Ridge Regression

分数岭回归

• 批准号: 2310208
• 负责人: Leonard Stefanski
• 金额: $ 32万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2310208&HistoricalAwards=false
• 关键词: Fractional; Ridge; Regression

Technological advances make it possible to collect enormous amounts of data. Implications for how businesses run (online retailing, precision manufacturing, social media), how science is conducted (environmental science, climate modeling, chemoinformatics, biotechnology, engineering), and how governments operate (health care, public safety, homeland security, national defense, agriculture production) are correspondingly enormous. For many uses of massive data sets, not all of the available information is relevant. For example, of the estimated 100,000 human genes, often only a handful are relevant to understanding a particular disease and developing a cure (the challenge is identifying the handful of relevant genes). A key feature in many big-data explorations is the identification and deemphasis of superfluous information with the corresponding identification and accentuation of the most relevant information (separating the wheat from the chaff). Fractional Ridge Regression (FRR) is designed to improve both prediction and interpretability of statistical analyses of large data sets relative to statistical methods currently in use. FRR improves the identification and extraction of relevant information from large data sets thereby improving the many areas of business, science, and government policy that rely on the analysis and understanding of large data sets. With nearly limitless applications, FRR research is ideal for engaging diverse statistics students in research projects. Computing algorithms and statistical software will make FRR available to researchers in all disciplines, thereby multiplying its potential benefits to education and diversity in numerous areas of data science. The investigator will identify sub-projects for undergraduate and graduate students with attention to student recruitment from under-represented groups.Fractional ridge regression joins ridge regression and the lasso in the statistician's regression modeling toolbox. Ridge regression was introduced by Hoerl and Kennard in 1970 and twenty-six years later was followed by the introduction of the lasso by Tibshirani. The body of research ensuing from these seminal papers is staggering, and has contributed immensely to our understanding of shrinkage and selection methodology and to the practice of regression modeling in many areas of science. In some applications of regression modeling the goal is simply to achieve the best possible predictions of future response values. In other applications, interpretation is important as a way to guide understanding of the process under investigation. Ridge regression is very good at prediction, although it is often eclipsed by the lasso in terms of both prediction and interpretation because the lasso also allows for selection. Fractional ridge regression (FRR) improves both prediction (measured by mean square error) and interpretability (measured by variable selection specificity) relative to the lasso. FRR accomplishes these twin goals via a unique and clever penalty function that adaptively downweighs only a data-driven subset of regression model coefficients (a fraction), while allowing for the complementary subset of regression coefficients to vary freely in order to obtain an optimal fitted model.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

技术进步使收集海量数据成为可能。企业如何运作(在线零售、精密制造、社交媒体)、科学如何进行(环境科学、气候建模、化学信息学、生物技术、工程学)以及政府如何运作(医疗保健、公共安全、国土安全、国防、农业生产)的影响相应地是巨大的。对于海量数据集的许多用途，并不是所有可用的信息都是相关的。例如，在估计的10万个人类基因中，通常只有几个与了解特定疾病和开发治疗方法有关(挑战是识别少数相关基因)。许多大数据探索中的一个关键特征是识别和淡化多余信息，同时相应地识别和强调最相关的信息(将小麦和谷壳分开)。相对于目前使用的统计方法，分数岭回归(FRR)被设计用来提高对大数据集的统计分析的预测性和可解释性。FRR改进了从大数据集中识别和提取相关信息的能力，从而改进了商业、科学和政府政策的许多领域，这些领域依赖于对大数据集的分析和理解。具有几乎无限的应用，FRR研究是吸引不同统计专业学生参与研究项目的理想选择。计算算法和统计软件将使所有学科的研究人员都能使用FRR，从而使其在许多数据科学领域的教育和多样性方面的潜在好处成倍增加。研究人员将为本科生和研究生确定子项目，关注从代表性不足的群体中招募学生。分数岭回归在统计学家的回归建模工具箱中加入了岭回归和套索。岭回归是由Hoerl和Kennard在1970年引入的，26年后，Tibishani引入了套索。从这些开创性的论文中产生的研究是惊人的，并为我们理解收缩和选择方法以及在许多科学领域中的回归建模实践做出了巨大贡献。在回归建模的一些应用中，目标只是实现对未来响应值的最佳可能预测。在其他应用中，解释作为指导对调查过程的理解的一种方式是很重要的。岭回归非常擅长预测，尽管它在预测和解释方面经常被套索所掩盖，因为套索也允许选择。相对于套索，分数岭回归(FRR)提高了预测性(通过均方误差衡量)和可解释性(通过变量选择专一性衡量)。FRR通过一个独特而聪明的惩罚函数实现了这两个目标，该函数仅自适应地降低回归模型系数的一个数据驱动子集(分数)的权重，同时允许回归系数的互补子集自由变化，以获得最佳拟合模型。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。