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Sparse Regression Ensembles in Infinite and Finite Hypothesis Spaces
, 2000
"... We examine methods for constructing regression ensembles based on a linear program (LP). The ensemble regression function consists of linear combina tions of base hypotheses generated by some boostingtype base learning algorithm. Unlike the classification case, for regression the set of possible h ..."
Abstract

Cited by 18 (9 self)
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We examine methods for constructing regression ensembles based on a linear program (LP). The ensemble regression function consists of linear combina tions 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 semiinfinite 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 hypothesisspace 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 simplextype algorithm and the other adopts an exponential barrier approach. Furthermore, we give sufficient conditions for the base learning algorithm and the hypothesis set to be used for infinite regression ensembles. Computational resultsshow that these methods are extremely promising.
Adapting Codes and Embeddings for Polychotomies
, 2003
"... In this paper we consider formulations of multiclass problems based on a generalized notion of a margin and using output coding. This includes, but is not restricted to, standard multiclass SVM formulations. Differently from many previous approaches we learn the code as well as the embedding f ..."
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Cited by 17 (4 self)
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In this paper we consider formulations of multiclass problems based on a generalized notion of a margin and using output coding. This includes, but is not restricted to, standard multiclass SVM formulations. Differently from many previous approaches we learn the code as well as the embedding function. We illustrate how this can lead to a formulation that allows for solving a wider range of problems with e.g. many classes or even "missing classes". To keep our optimization problems tractable we propose an algorithm capable of solving them using twoclass classifiers, similar in spirit to Boosting.