Collaborative Research: New Theory and Methods for High-Dimensional Multi-Task and Transfer Learning Inference

在许多现代大数据应用中，数据往往来自不同的来源。为了提高预测或聚类的精度，多任务学习和迁移学习技术已被广泛使用，以利用不同任务之间可能的相似性。例如，为联邦储备经济数据库(FRED)等应用程序制定可靠的推断程序，以确定与典型宏观经济指标相关的重要宏观经济变量的潜在因素和个别构成，这一点至关重要。同样，对于阿尔茨海默病神经成像倡议(ADNI)和国家阿尔茨海默病协调中心(NACC)这样的数据库来说，早期发现和识别阿尔茨海默病等痴呆症的风险因素至关重要。在这些背景下，不同的经济指标或不同医院的患者可能会有某些相似之处。然而，如何为高维多任务学习和迁移学习开发灵活的推理程序在很大程度上仍然不清楚。该研究项目可能会对不同的领域产生潜在的重大影响，包括经济、商业、工程和医学。这些新的理论和方法的发展将为实际条件下的高维多任务和迁移学习推理建立严格的统计基础，并为数据科学应用中的各种研究人员和实践者提供可解释的、灵活的和健壮的工具。该项目还为研究生提供了研究培训机会。有监督和无监督环境下的高维多任务和迁移学习推理是统计机器学习和数据科学中具有挑战性的重要课题。在这个项目中，绩效指标通过进行系统研究来应对这些基本挑战，以通过三个相互关联的目标开发新的方法、算法、理论和应用程序。首先，PI计划研究基于高维流形的多任务学习推理，这涉及到学习位于低维流形上的多个任务的共享表示。该项目将开发健壮和可扩展的算法，可以处理高维数据并结合流形约束，为潜在奇异值分解(SVD)结构提供急需的推理工具。其次，PI计划处理高维稳健的多任务聚类推理，其目标是在存在离群值和噪声的情况下同时对来自多个任务的数据进行聚类。该项目将开发新的健壮的多任务集群算法，可以处理高维数据和离群点任务。第三，PI计划研究高维自适应和稳健的多任务学习，以及从相似的线性表示中迁移学习，这涉及到学习共享相似线性结构的多个任务的共享表示。在这里，该项目将开发自适应和健壮的算法，可以处理高维数据，适应不同的噪声水平，并通过类似的线性表示传递知识。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。

In many modern big data applications, data is often collected from diverse sources. To improve prediction or clustering accuracy, multi-task learning and transfer learning techniques have been employed widely to leverage the possible similarities across different tasks. For example, it is of crucial importance to develop reliable inference procedures for applications such as the Federal Reserve Economic Database (FRED) to identify latent factors and individual compositions of significant macroeconomic variables associated with typical macroeconomic indicators. Similarly, for databases like the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the National Alzheimer's Coordinating Center (NACC), early detection and risk factor identification of dementia, such as Alzheimer's disease, is vital. In these contexts, different economic indicators or patients in different hospitals may share certain similarities. However, it remains largely unclear how to develop flexible inference procedures for high-dimensional multi-task learning and transfer learning. The research project can have potentially significant impacts across diverse fields, including economics, business, engineering, and medicine. These new theoretical and methodological developments will build rigorous statistical foundations for high-dimensional multi-task and transfer learning inference under practical conditions, and provide interpretable, flexible, and robust tools for various researchers and practitioners in data science applications. The project also provides research training opportunities for graduate students. High-dimensional multi-task and transfer learning inference under both supervised and unsupervised settings are challenging and important topics in statistical machine learning and data science. In this project, the PIs address these fundamental challenges by conducting systematic studies to develop novel methodologies, algorithms, theories, and applications through three interrelated aims. First, the PIs plan to investigate high-dimensional manifold-based multi-task learning inference, which involves learning a shared representation of multiple tasks that lie on a low-dimensional manifold. the project will develop robust and scalable algorithms that can handle high-dimensional data and incorporate manifold constraints to provide much-needed inference tools for the latent singular value decomposition (SVD) structures. Second, the PIs plan to tackle high-dimensional robust multi-task clustering inference, where the goal is to simultaneously cluster data from multiple tasks in the presence of outliers and noise. The project will develop novel robust multi-task clustering algorithms that can handle high-dimensional data and outlier tasks. Third, the PIs plan to investigate high-dimensional adaptive and robust multi-task learning and transfer learning from similar linear representations, which involves learning a shared representation of multiple tasks that share similar linear structures. Here, the project will develop adaptive and robust algorithms that can handle high-dimensional data, adapt to different noise levels, and transfer knowledge across similar linear representations.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.