统计学系系列讲座之339-340期

统计学系系列讲座之339期

时　间：2019年5月22日（星期三）16:15-17:15

地　点：李达三楼105室

主持人：张新生教授 复旦大学管理学院统计学系

主　题：Communication-Efficient Accurate Statistical Estimation

主讲人：Prof. Jianqing Fan　Princeton University　

简　介：

Dr. Jianqing Fan, is a statistician, financial econometrician, and data scientist. He is Frederick L. Moore '18 Professor of Finance, Professor of Statistics, and Professor of Operations Research and Financial Engineering at the Princeton University where he chaired the department from 2012 to 2015. He is the winner of The 2000 COPSS Presidents' Award. He got elected to Academician from Academia Sinica in 2012. Professor Fan is a co-editor of Journal of Econometrics and an associate editor of and Journal of the American Statistical Association (1996--), among others, was the co-editor(-in-chief) of the Annals of Statistics (2004-2006) and an editor of Probability Theory and Related Fields (2003-2005), Econometrical Journal (2007-2012).

摘　要：

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)

统计学系系列讲座之340期

时　间：2019年5月28日（星期二）16:00-17:00

地　点：史带楼302室

主持人：夏寅教授 复旦大学管理学院统计学系

主　题：Singular Value Decomposition for High-dimensional High-order Data

主讲人：Ph.D. Anru Zhang　Department of Statistics, University of Wisconsin-Madison

简　介：

Anru Zhang is currently an assistant professor at the Department of Statistics, University of Wisconsin-Madison. He is also affiliated to Machine Learning Group and Institute for Foundations of Data Science at UW-Madison. He obtained the PhD degree from University of Pennsylvania in 2015 and the bachelor’s degree from Peking University in 2010. His current research interests include High-dimensional Statistical Inference, Tensor Data Analysis, and Statistical Learning Theory. He received grants from the National Science Foundation and National Institute of Health.

摘　要：

High-dimensional high-order data arise in many modern scientific applications including genomics, brain imaging, and social science. In this talk, we consider the methods, theories, and computations for tensor singular value decomposition (tensor SVD), which aims to extract the hidden low-rank structure from high-dimensional high-order data. First, comprehensive results are developed on both the statistical and computational limits for tensor SVD under the general scenario. This problem exhibits three different phases according to signal-noise-ratio (SNR), and the minimax-optimal statistical and/or computational results are developed in each of the regimes. In addition, we further consider the sparse tensor singular value decomposition which allows more robust estimation under sparsity structural assumptions. A novel sparse tensor alternating thresholding algorithm is proposed. Both the optimal theoretical results and numerical analyses are provided to guarantee the performance of the proposed procedure.

 统计学系 

2019-5-17