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

• Activity Number: 23 - Recents Advances in Statistical Learning and Network Data Analysis
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Yufeng Liu*
• Companies: University of North Carolina at Chapel Hill
• Keywords: Individual Treatment Rule; Optimal Decisons; Personalized Medicine; Supervised Learning; Value Functions

Abstract

In modern predictive modeling process, budget constraints become a very important consideration due to the high cost of collecting data. 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. 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. Both theoretical and numerical studies are used to demonstrate the effectiveness of the proposed method.