CAREER: New Techniques for Statistical Learning and Multivariate Analysis

许多科学领域的新技术导致数据集的复杂性和规模越来越大，测量和存储这些大量数据的能力远远超过了分析数据以做出可重复的科学发现的能力。例子包括基因组学和蛋白质组学、神经成像和神经记录数据。分析这些大的生物医学数据对于发现疾病生物标志物，在个性化医疗方面取得进展以及理解复杂生物系统的基本工作至关重要。在这项工作中，我们寻求开发和研究新的统计学习和多元分析技术，直接解决从大科学数据中获得发现的关键未解决问题。此外，我们将使用统计学习技术，通过开发一个在线个性化学习系统，为作业和内容交付改进入门统计教育。更具体地说，这项工作将侧重于使用大规模稀疏优化算法来激发和开发一个新的统计学习框架，该框架将被证明对高维和高度相关的数据具有卓越的经验和理论性能。这样的数据在基因组学和神经影像学中很常见；这些新技术将用于识别潜在的基因组药物靶点，模拟遗传和大脑网络，以及从神经成像和神经记录数据中解码大脑。我们还将使用克罗内克积协方差为耦合矩阵和张量数据开发新的多变量分析模型。这些技术将用于在整合基因组学数据中寻找联合模式，并找到指示行为或临床协变量的大脑活动模式。总的来说，这项工作将开发几种急需的统计技术来理解大型和复杂的数据，对基因组学和脑科学产生直接影响，这些技术将与科学家合作应用，并导致入门统计教育的改进。该奖项由数学和物理科学理事会（MPS）数学科学部（DMS）和生物科学理事会（BIO）综合有机体系统（IOS）和新兴前沿（EF）部门共同资助。

New technologies in many scientific sectors have led to data sets of increasing complexity and size, where the ability to measure and store these vast troves of data has far outpaced the ability to analyze the data to make reproducible scientific discoveries. Examples include genomics and proteomics, neuroimaging, and neural recordings data. Analyzing this big biomedical data is critical to discovering disease biomarkers, making advances in personalized medicine, and understanding the basic workings of complex biological systems. In this work, we seek to develop and study novel statistical learning and multivariate analysis techniques that directly address unresolved problems critical for making discoveries from big scientific data. Additionally, we will use statistical learning techniques to improve introductory statistics education by developing an online personalized learning system for assignment and content delivery. More specifically, this work will focus on using algorithms for large-scale sparse optimization to inspire and develop a new framework for statistical learning that will prove to have superior empirical and theoretical performance for high-dimensional and highly correlated data. Such data is common in genomics and neuroimaging; the new techniques will be used to identify potential genomic drug targets, to model genetic and brain networks, and for brain decoding from neuroimaging and neural recordings data. We will also use Kronecker product covariances to develop new multivariate analysis models for coupled matrix and tensor data. These techniques will be used to find joint patterns in integrative genomics data and find patterns of brain activity indicative of behavioral or clinical covariates. Overall, this work will develop several critically needed statistical techniques to understand large and complex data, have direct impacts in genomics and brain science where the techniques will be applied in collaboration with scientists, and lead to improvements in introductory statistics education. This award is co-funded by the Directorate for Mathematical and Physical Sciences (MPS) Division of Mathematical Sciences (DMS) and the Directorate for Biological Sciences (BIO) Divisions of Integrative Organismal Systems (IOS) and Emerging Frontiers (EF).