DMS/NIGMS 1: Multilevel stochastic orthogonal subspace transformations for robust machine learning with applications to biomedical data and Alzheimer's disease subtyping

晚发性阿尔茨海默病(AD)是最常见的痴呆症形式，据估计，目前有650万65岁及以上的美国人患有AD--到2050年，这一数字将翻一番。超过35%的85岁以上的人患有AD，是65岁以上美国人的第五大死亡原因，每年造成的社会成本超过3400亿美元。在过去的几年里，大量的研究强调，在遗传学、临床症状和生化途径方面，可能存在不同形式的AD和AD相关痴呆。不同的过程和分子途径可导致多种临床和生理亚型的AD。这可能有助于解释许多(失败的)临床试验，这些试验通常针对众所周知的淀粉样蛋白途径和基因。为了开发更新、更有效、更安全的治疗方法，需要为AD治疗提供多个新的临床靶点，以增加成功率。确定特定AD亚型背后的这种多个过程/途径的需要至关重要。发现这些将允许开发针对特定AD形式的有针对性的诊断和治疗。这一多方面项目的研究人员将利用从不同人群获得的遗传、蛋白质和脑成像数据，开发一种数学基础和方案，以确定AD亚型和为这些亚型量身定做的潜在药物靶点。这些发现将对医学界有价值，并将有助于进一步了解许多不同形式的AD，并推动精确医学方法的发展。调查人员还致力于培训、发展和培养学生在这些领域的专业知识，为他们提供宝贵的学习机会。越来越多地利用和分析广泛的数据集，特别是在医学和生物领域，突出表明需要先进和精确的数据分析方法。在这种背景下，基于机器学习(ML)的统计推理正迅速成为计算增值的基石。然而，尽管人们一直致力于改进ML算法，但特征工程的重要性却被忽视了。因此，人们对开发一种新的用于特征构造的数学框架越来越感兴趣。关键的洞察力是将数据视为随机场在合适的Bochner函数空间中的实现。通过构建一个新的坐标系，研究人员可以揭示定义良好的模式，这些模式可以显著提高现有ML算法的准确性。该项目的目标包括：(I)开发一种用于构造创新特征的数学理论和协议，以更好地区分输入数据的潜在随机行为，使用多层空间和Bochner空间的Karhunen-Love(KL)展开。(Ii)分析和优化这种多层特征结构的参数，以显著提高ML算法的性能，特别是在处理复杂和具有挑战性的输入时。(Iii)从现有的阿尔茨海默氏病(AD)广泛的数据集中，如全基因组的遗传、基因组、蛋白质组、脑成像数据和人口规模的电子健康记录数据，确定基于ML的阿尔茨海默病(AD)亚型。据估计，有650万65岁及以上的美国人患有阿尔茨海默病，这一领域的工作可能会产生非常重大的影响。特别是，准确的病例分类可以极大地加速新靶向AD药物的成功开发。这一裁决反映了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。

Late-onset Alzheimer's Disease (AD) is the most common form of dementia, with an estimated 6.5 million Americans aged 65 and older living with AD today - this number will double by 2050. AD occurs in more than 35% of individuals over the age of 85 and is the fifth leading cause of death among Americans over the age of 65, with a resulting societal cost of more than $340 billion per year. Over the past years, numerous studies have highlighted that there are likely different forms of AD and AD-related dementia in the context of genetics, clinical symptoms, and biochemical pathways. Different processes and molecular pathways can lead to many clinical and physiological subtypes of AD. This may help to explain numerous (failed) clinical trials which have usually targeted the well-known amyloid pathways and genes. To develop newer, more effective, and safer treatments, multiple new clinical targets for AD treatment are needed to increase probabilities of success. The need to identify such multiple processes/pathways underlying specific AD subtypes is crucial. Discovering these will allow the development of targeted diagnosis and treatment that is adapted and personalized to particular AD forms. The investigators in this multifaceted project will leverage the availability of genetic, protein and brain imaging data obtained from diverse populations to develop a mathematical foundation and protocol for identifying AD subtypes and potential drug targets tailored to these subtypes. The findings will be valuable to the medical community and will contribute to further understanding of the many different forms of AD and to advancing precision medicine approaches. The investigators are also committed to training, developing and nurturing students' expertise in these areas, providing them with valuable learning opportunities. The increasing utilization and analysis of extensive datasets, particularly in medical and biological domains, underscores the need for advanced and precise data analysis methods. In these contexts, Machine Learning (ML)-based statistical inference is rapidly becoming a cornerstone of computational value addition. However, while much attention has been devoted to refining ML algorithms, the significance of feature engineering has been somewhat overlooked. Consequently, there is a growing interest in developing a novel mathematical framework for feature construction. The key insight is to treat data as realizations of a random field in a suitable Bochner function space. By constructing a new coordinate system, the investigators can unveil well-defined patterns that can significantly enhance the accuracy of existing ML algorithms. The objectives of this project include: (I) Developing a mathematical theory and protocol for constructing innovative features to better discriminate underlying stochastic behaviors of input data, employing multilevel spaces and the Karhunen-Loeve (KL) expansion for Bochner spaces. (II) Analyzing and optimizing the parameters of such multilevel feature constructions to markedly enhance the performance of ML algorithms, especially when dealing with complex and challenging inputs. (III) Identifying ML-based subtypes of Alzheimer's Disease (AD) from available extensive AD datasets such as genome-wide genetic, genomic, proteomic, brain imaging data and population-scale electronic health record data. With an estimated 6.5 million Americans 65 and older living with AD, the impact of work in this area can potentially be very significant. Particularly, accurate subtyping of cases can greatly accelerate successful development of new targeted AD drugs.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.