Computational and Communication Efficient Distributed Statistical Methods with Theoretical Guarantees

在许多当代数据分析环境中，假设整个数据集在中央位置可用是昂贵的和/或不可行的。在计算数学和机器学习的最新研究中，分布式优化和分布式学习（即机器学习）取得了长足的进步。另一方面，经典的统计方法、理论和计算通常基于这样的假设：整个数据在一个中心位置可用。这是现代统计知识的一个重大缺陷。分布式推理的统计方法和理论还不发达。 PI 将开发新的计算和通信高效的分布式统计方法。他将研究这些分布式统计估计器的理论保证。将探索和论证这些方法在广泛应用领域的适用性和需求。这项研究可能会对医疗保健、供应链行业、零售和服务业等产生影响。基于应用数学和机器学习领域的最新成果，PI将探索为分布式数据和聚合推理（即分布式推理）开发的统计过程的理论、算法和应用，同时考虑相关估计器的存储、计算复杂性和统计特性。该项目将开发实用模型、统计理论以及计算效率高且可证明正确的算法，可以帮助科学家进行更有效的分布式数据分析。将深入研究这些方法的统计特性，包括渐近特性分析、有限样本情况下的模拟研究以及在一些实际应用中建立有效性。博士生将参与这项研究。课程模块将被开发并公开发布。

In many contemporary data-analysis settings, it is expensive and/or infeasible to assume that the entire data set is available at a central location. In recent works of computational mathematics and machine learning, great strides have been made in distributed optimization and distributed learning (i.e., machine learning). On the other hand, classical statistical methodology, theory, and computation are typically based on the assumption that the entire data are available at a central location; this is a significant shortcoming in modern statistical knowledge. The statistical methodology and theory for distributed inference are underdeveloped. The PI will develop new distributed statistical methods that are computation and communication efficient. He will study the theoretical guarantees of these distributed statistical estimators. The applicability and need of these methods in a wide spectrum of application domains will be explored and demonstrated. This research can have impacts in healthcare, supply chain industries, retail and services, and many more. Based on recent works in applied mathematics and machine learning, the PI is to explore theory, algorithms, and applications of statistical procedures that are developed for distributed data and aggregated inference (i.e., distributed inference), with considerations on the storage, computational complexity, and statistical properties of the relevant estimators. The project will develop practical models, statistical theory, and computationally efficient and provably correct algorithms that can help scientists to conduct more effective distributed data analysis. Statistical properties of these methods will be thoroughly studied, including analysis of asymptotic properties, simulation studies in finite sample cases, and establishment of effectiveness in some real applications. PhD students will be involved in the research. Course modules will be developed and made available publicly.