LEAPS-MPS: Functional Data Analysis for Conditional Quantiles with Applications in Medical Studies

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。功能数据分析(FDA)研究包含在时间和空间域等连续统一体上变化的信息的数据，这些数据对许多现实世界的应用具有巨大的影响，包括金融、自然语言处理、电网稳定，特别是医疗领域。例如，功能磁共振成像(FMRI)和脑电(EEG)等数据类型提供了对大脑和头皮不同位置的多种观察，是FDA的主要竞争者。然而，fMRI和EEG数据往往都是高度倾斜的，可能包含异常值；目前，传统的FDA方法无法全面和准确地分析它们。尽管FDA的文献最近取得了许多进展，但这一领域仍处于初级阶段，还有许多潜力有待发现。该项目通过开发一种新的方法来分析功能数据，从而解决了这一差距，该方法能够更好地解释严重的偏度和异常观测。这种方法将被用来检查fMRI和EEG数据，目的是研究两种重要的神经疾病：(1)注意力缺陷多动障碍(ADHD)和(2)酒精中毒。神经障碍表现为大脑活动的特征是截然不同的生化和电行为，其中输出要么异常高，要么异常低，因此使用这种新方法可以更有效地进行分析。研究结果将被合并到开源软件中，用于可重复性和进一步的研究，并鼓励医学界未来可能的合作。一个新的暑期研究项目将支持来自代表性不足背景的学生，他们将分析fMRI和EEG数据集，并将通过公共传播向医学界提供建议和建议。这一经历将改善学生对STEM职业的态度，帮助他们发展21世纪劳动力所需的技能，并鼓励他们寻求更高的学位机会。该项目还将提供研究生水平的研究培训机会。函数数据的无限维特性促使降维技术的使用，而医学数据中经常遇到的偏斜和异常观察需要使用分位数回归(QR)。尽管FDA最近取得了进展，但目前还没有关于FDA降维和QR的交集的工作。因此，该项目通过(1)开发具有无限维函数预测因子的QR降维技术，(2)扩展该方法以包括医学研究中常见的其他范畴预测因子，以及(3)通过对ADHD和酒精中毒的医学障碍的调查，将该方法整合到学生的训练中，以解决这一差距。这项工作将开发计算效率高的算法，这些算法将通过PI的现有软件传播。最后，这项研究将为从事罕见疾病工作的医学研究人员带来新的迫切需要的统计方法，并将帮助临床医生获得更具可操作性的见解。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。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Functional Data Analysis (FDA) investigates data containing information that varies over a continuum such as the temporal and spatial domains, with tremendous implications for many real-world applications, including finance, natural language processing, electric grid stabilization, and especially the medical field. For example, data types such as functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) provide multiple observations for different locations of the brain and scalp, and are prime contenders of FDA. However, both fMRI and EEG data are often highly skewed and may contain outliers; currently, traditional FDA methods are not able to analyze them fully and accurately. Despite the many recent advancements in the FDA literature, this area is still in its infancy with much potential yet to be uncovered. The project addresses this gap by developing a novel approach for analyzing functional data that is better able to account for heavy skewness and outlying observations. This approach will be used to examine both fMRI and EEG data with the goal of investigating two important neurological disorders: (1) attention deficit hyperactivity disorder (ADHD) and (2) alcoholism. Neurological disorders exhibit brain activity characterized by drastically different biochemical and electrical behavior where the output is either atypically high or atypically low, and hence more effectively analyzed using this new method. The results will be incorporated into open-source software for reproducibility and further research, and for encouraging possible future collaborations in the medical community. A new summer research program will support students from underrepresented backgrounds who will analyze the fMRI and EEG data sets and will provide recommendations and suggestions to the medical community through public dissemination. This experience will improve students’ attitudes towards STEM careers, help them develop skills necessary for the 21st-century workforce, and encourage them to seek advanced degree opportunities. The project will provide research training opportunities at the graduate level as well. The infinite dimensional nature of functional data motivates the use of dimension reduction techniques, whereas the skewness and outlying observations often encountered in medical data require the use of quantile regression (QR). Despite recent advancements in FDA, there is no current work on the intersection of both dimension reduction and QR for FDA. Therefore, the project addresses this gap by (1) developing a dimension reduction technique for QR with infinite dimensional functional predictors, (2) extending the method to incorporate additional categorical predictors that are common in medical studies, and (3) integrating the methods into students’ training through investigation of the medical disorders of ADHD and alcoholism. This work will develop computationally efficient algorithms that will be disseminated through the PI’s existing software. Finally, this research will lead to new critically needed statistical methods for medical researchers working with rare diseases and will help clinicians to garner more actionable insight.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.