Statistics Seminar (2019-13)

Title: Communication-Efficient Accurate Statistical Estimation

Speaker: Jianqing Fan, Princeton University

Time: Tuesday, May 28, 10:00-11:00

Place: Room 214, Guanghua Building 2

Abstract:

When the data are stored in a distributed manner, direct application of traditional statistical inference procedures is often prohibitive due to communication cost and privacy concerns. This paper develops and investigates two Communication-Efficient Accurate Statistical Estimators (CEASE), implemented through iterative algorithms for distributed optimization. In each iteration, node machines carry out computation in parallel and communicates with the central processor, which then broadcasts aggregated gradient vector to node machines for new updates. The algorithms adapt to the similarity among loss functions on node machines, and converge rapidly when each node machine has large enough sample size. Moreover, they do not require good initialization and enjoy linear converge guarantees under general conditions. The contraction rate of optimization errors is derived explicitly, with dependence on the local sample size unveiled. In addition, the improved statistical accuracy per iteration is derived. By regarding the proposed method as a multi-step statistical estimator, we show that statistical efficiency can be achieved in finite steps in typical statistical applications. In addition, we give the conditions under which one-step CEASE estimator is statistically efficient. Extensive numerical experiments on both synthetic and real data validate the theoretical results and demonstrate the superior performance of our algorithms.

(Joint work with Yongyi Guo and Kaizheng Wang)

Introduction:

范剑青（Jianqing Fan），现为复旦大学大数据学院教授、院长，普林斯顿大学Frederick L. Moore’18金融学讲座教授。2000年荣获COPSS总统奖（国际统计学领域最高奖项），2006年荣获洪堡基金会终身成就奖，2007年荣获晨兴华人数学家大会应用数学金奖，2009年荣获在美国文理与艺术界著名的GUGGENHEIM Fellow，2012年当选台湾“中央研究院”院士，2013年获泛华统计学会 （International Chinese Association）的“许宝禄奖”，2014年荣获英国皇家统计学会授予的“Guy Medal”银质奖章，2018年荣获诺特资深学者奖（Noether Senior Scholar Award），现为国际统计学会（International Statistical Institute）会士、国际数理统计学会（Institute of Mathematical Statistics）会士、美国统计学会（American Statistical Association）会士、美国科学促进会（American Association for the Advancement of Science）会士、计量金融学会（The Society for Financial Econometrics）会士。主要研究领域为高维统计、机器学习、大数据科学、经济学、金融学、生物信息等。学术成果发表在Annals of Statistics，Journal of American Statistical Association，Econometrica, Journal of Econometrics，Journal of Financial Economics等国际一流期刊上。目前为国际一流期刊Journal of Econometrics的联合主编，Journal of American Statistical Association的副主编。

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