Speaker: Dr. Ying Cui (University of Southern California)

Title:Composite Difference-Max Programs for Modern Statistical Estimation Problems

Time: Fri, Aug.10, 2018 , PM:3:00-4:00.

Location: Room 4318, Building No.4, Wushan Campus

Abstract：

  Many modern statistical estimation problems are defined by three major components: a statistical model that postulates the dependence of an output variable on the input features; a loss function measuring the error between the observed output and the model predicted output; and a regularizer that controls the overfitting and/or variable selection in the model.We study the sampled version of this generic statistical estimation problem where the model parameters are estimated by empirical risk minimization, which involves the minimization of the empirical average of the loss function at the data points weighted by the model regularizer. In our setup we allow all three component functions to be of the difference-of-convex (dc) type and illustrate them with a host of commonly used examples, including those in continuous piecewise affine regression and in deep learning with piecewise affine activation functions. We describe a non-monotone majorization-minimization (MM) algorithm for solving the unified nonconvex, non-differentiable optimization problem which is formulated as a specially structured composite dc program of the pointwise max type, and present convergence results to a directional stationary solution. An efficient semi smooth Newton method is proposed to solve the dual of the MM sub-problems. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm and the superiority of continuous piecewise affine regression over the standard linear model.

Biography:

  Ying Cui is currently a postdoc research associate in Department of Industrial and Systems Engineering at University of Southern California, working with Professor Jong-Shi Pang. She received her Ph.D from Department of Mathematics, National University of Singapore in 2016, under the supervisions of Professor Defeng Sun and Professor Chenlei Leng.