The nonparametric maximum likelihood estimation (NPMLE) is a classic and important method to estimate the mixture models from finite observations. The discretization of the infinite dimensional probability measure with a fixed support in the NPMLE leads to a finite dimensional convex optimization problem. Although can be solved by off-the-shelf interior point based solvers, the algorithm does not scale well with the number of grid points and the number of observed data points. In this talk, we propose an efficient and scalable semismooth Newton based augmented Lagrangian method (ALM). By carefully exploring the structure of the ALM subproblem, we show that the computational cost of the generalized Hessian (second order information) is independent of the number of grid points. Extensive numerical experiments are conducted to show the effectiveness of our approach.

Papers related to the talk:
https://arxiv.org/abs/2208.07514

Zhang Yangjing is an assistant professor in Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Before September 2021, she was a research fellow in National University of Singapore. Zhang obtained her Ph.D. degree from National University of Singapore in May 2019, and a B.S. in mathematics from Tsinghua University in 2014. Her current research is focused on large scale sparse optimization problems, the design of efficient algorithms for statistical models and graphical models.

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg