Sparse Regression Ensembles in Infinite and Finite Hypothesis Spaces

We examine methods for constructing regression ensembles based on a linear program (LP). The ensemble regression function consists of linear combinations of base hypotheses generated by some boostingtype base learning algorithm. Unlike the classification case, for regression the set of possible hypotheses producible by the base learning algorithm may be infinite. We explicitly tackle the issue of how to define and solve ensemble regression when the hypothesis space is infinite. Our approach is based on a semi-infinite linear program that has an infinite number of constraints and a finite number of variables. We show that the regression problem is well posed for infinite hypothesis spaces in both the primal and dual spaces. Most importantly, we prove there exists an optimal solution to the infinite hypothesis space problem consisting of a finite number of hypothesis. We propose two algorithms for solving the infinite and finite hypothesis problems. One uses a column generation simplex-t...

• Type: Journal
• Year: 2002
• Where: ML
• Authors: Gunnar Rätsch, Ayhan Demiriz, Kristin P. Bennett
• Keywords: Algorithm, Infinite, Infinite Hypothesis, Machine Learning, ML 2002