Computational and Communication Efficient Distributed Statistical Methods with Theoretical Guarantees

在许多当代数据分析设置中，假设整个数据集在中心位置可用是昂贵的和/或不可行的。在最近的计算数学和机器学习的工作中，在分布式优化和分布式学习（即机器学习）方面取得了很大的进步。另一方面，经典的统计方法、理论和计算通常是基于这样的假设：所有的数据都在一个中心位置；这是现代统计知识的一个重大缺陷。分布推理的统计方法和理论还不发达。PI将开发新的分布式统计方法，这些方法具有计算和通信效率。他将研究这些分布统计估计的理论保证。这些方法在广泛的应用领域的适用性和需求将被探索和论证。这项研究可以对医疗保健、供应链行业、零售和服务等产生影响。基于最近在应用数学和机器学习方面的工作，PI旨在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，同时考虑到相关估计器的存储，计算复杂性和统计特性。该项目将开发实用模型、统计理论和计算效率高且可证明正确的算法，帮助科学家进行更有效的分布式数据分析。这些方法的统计性质将被深入研究，包括渐近性质的分析，有限样本情况下的模拟研究，以及在一些实际应用中的有效性。博士研究生将参与研究。课程模块将被开发并公开提供。

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.