Report topic: Fast algorithm and asymptotic theory analysis of high-dimensional precision matrix estimation
Reporter: Wang Cheng, researcher, Shanghai Jiaotong University
Reporting time: 13:30-14:30, November 26, 2020
Report location: Tencent Conference ID: 488 759 405 Conference password: 654321
School contact: Zhu Fukang fzhu@jlu.edu.cn
Report summary:
In high-dimensional data analysis, estimating the covariance matrix and its inverse precision matrix is a very important basic problem. This report shares some recent research results on high-dimensional precision matrix estimation. The first part introduces a result of the algorithm; Based on the standard ADMM algorithm, the theoretically optimal algorithm is designed for the quadratic loss form estimation method. The second part of the report re-derives a theoretical consistency result based on the LASSO precision matrix estimation method from the perspective of matrix estimation under the condition of asymptotic sparseness. This theoretical result does not require an irrepresentable condition and is suitable for asymptotically sparse matrices. As applications, we consider the problem of precision matrix estimation in heavy-tailed data, non-parametric normal data, and matrix data.
Brief introduction of the speaker:
Wang Cheng graduated from the University of Science and Technology of China with a Ph.D. in 2013 and won the Special Award of the President of the Chinese Academy of Sciences. In September 2014, he joined the School of Mathematical Sciences of Shanghai Jiaotong University as a special researcher. The main research direction is random matrix theory and application, statistical inference of high-dimensional covariance matrix, etc. He has published more than ten academic papers in Statistica Sinica, Electronic Journal of Statistics and other journals in the field of statistics. Presided over the National Natural Science Foundation of China Youth Fund, Shanghai Youth Science and Technology Talents Sailing Program and three corporate projects, and participated in many national natural science fund key projects and general projects.
