Ensemble Methods for Convex Regression with Applications to Geometric Programming Based Circuit Design

Lauren Hannah, David B. Dunson

Abstract: Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods (Hannah and Dunson, 2011; Magnani and Boyd, 2009) are fast and scalable, but can have instability when used to approximate constraints or objective functions for optimization. Ensemble methods, like bagging, smearing and random partitioning, can alleviate this problem and maintain the theoretical properties of the underlying estimator. We empirically examine the performance of ensemble methods for prediction and optimization, and then apply them to device modeling and constraint approximation for geometric programming based circuit design.