大数据学院、统计学系联合学术报告

Abstract:

High-dimensional sparse learning and analysis of Big Data data pose significant challenges on computation and communication.  Scalable statistical procedures need to take into account both statistical errors and computing resource constraints.  This talk illustrate this idea by using two important examples in statistical machine learning.  The first one is to solve sparse learning via a computational framework named  iterative local adaptive  majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional sparse models via a family of folded concave penalized quasi-likelihood. The algorithmic complexity and statistical errors are explicitly given and we show that the algorithm achieves the optimal statistical error rate under the weakest signal strength assumptions. The second problem is to study distributed PCA with communication constraints:  each node machine computes the top eigenvectors and communicates to the central server; the central server then aggregates the information transmitted from the node machines and conducts another PCA based on the aggregated information.  We investigate the bias and variance for such a distributed PCA.  We derive the rate of convergence for distributed PCA, which depends explicitly on effective rank, eigen-gap, and the number of machines, and show that the distributed PCA performs as well as the whole sample PCA, even without full access of whole data.

Bio:

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).