#### High-dimensional Cost-constrained Regression via Non-convex Optimization

Yufeng Liu，(University of North Carolina at Chapel Hill)

2018.06.26, 8:30-9:30, N109

【Abstract】In modern predictive modeling process, budget constraints become a very important consideration due to the high cost of collecting data using new techniques such as brain imaging and DNA sequencing. This motivates us to develop new and efficient high-dimensional cost constrained predictive modeling methods. In this talk, to address this challenge, we first study a new non-convex high-dimensional cost-constrained linear regression problem, that is, to find the cost-constrained regression model with the smallest expected prediction error among all models satisfying a budget constraint. The non-convex budget constraint makes this problem NP-hard. In order to estimate the regression coefficient vector of the cost-constrained regression model, we propose a new discrete extension of recent first-order continuous optimization methods. We further show some extensions of our proposed method for statistical learning problems using loss functions with Lipschitz continuous gradient. It can be also extended to problems with groups of variables or multiple constraints. Theoretically, we prove that the series of the estimates generated by our iterative algorithm converge to a first-order stationary point, which can be a globally optimal solution to the nonconvex high-dimensional cost-constrained regression problem. Computationally, our numerical studies show that the proposed method can solve problems of fairly high dimensions and has promising estimation, prediction, and model selection performance.