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An Asymptotic Analysis of Random Partition Based Minibatch Momentum Methods for Linear Regression Models

发布日期:2022-12-22点击量:

报告题目:

An Asymptotic Analysis of Random Partition Based Minibatch Momentum Methods for Linear Regression Models

报告人:

王汉生 教授

报告时间:

2022年12月30日周五 下午3:00

报告地点:

腾讯会议 ID 523-3915-6716


报告摘要:

Momentum methods have been shown to accelerate the convergence of the standard gradient descent algorithm in practice and theory. In particular, the random partition based minibatch gradient descent methods with momentum (MGDM) are widely used to solve large-scale optimization problems with massive datasets. Despite the great popularity of the MGDM methods in practice, their theoretical properties are still underexplored. To this end, we investigate the theoretical properties of MGDM methods based on the linear regression models. We first study the numerical convergence properties of the MGDM algorithm and derive the conditions for faster numerical convergence rate. In addition, we explore the relationship between the statistical properties of the resulting MGDM estimator and the tuning parameters. Based on these theoretical findings, we give the conditions for the resulting estimator to achieve the optimal statistical efficiency. Finally, extensive numerical experiments are conducted to verify our theoretical results.

报告人简介:

王汉生,北京大学光华管理学院商务统计与经济计量系,教授,博导,全国工业统计学教学研究会青年统计学家协会创始会长,美国统计学会(ASA)Fellow,国际统计协会(ISI) Elected Member。先后历任9个国际学术期刊副主编(Associate Editor)。在国内外各种专业杂志上发表文章100+篇,并合著有英文专著共1本,(合)著中文教材4本。爱思唯尔中国高被引学者学者(数学类,2014-2019;应用经济学类:2020;统计学类2021)。

主办单位:

数学科学学院、交叉科学研究院、北京国家应用数学中心