In practical applications, machine learning algorithms are often needed to learn classifiers that optimize domain specific performance measures. Previously, the research has focused on learning the needed classifier in isolation, yet learning nonlinear classifier for nonlinear and nonsmooth performance measures is still hard. In this paper, rather than learning the needed classifier by optimizing specific performance measure directly, we circumvent this problem by proposing a novel two-step approach called CAPO, namely, to first train nonlinear auxiliary classifiers with existing learning methods and then to adapt auxiliary classifiers for specific performance measures. In the first step, auxiliary classifiers can be obtained efficiently by taking off-the-shelf learning algorithms. For the second step, we show that the classifier adaptation problem can be reduced to a quadratic program problem, which is similar to linear @math and can be efficiently solved. By exploiting nonlinear auxiliary classifiers, CAPO can generate nonlinear classifier which optimizes a large variety of performance measures, including all the performance measures based on the contingency table and AUC, while keeping high computational efficiency. Empirical studies show that CAPO is effective and of high computational efficiency, and it is even more efficient than linear @math .
@cite_23: An up-to-date, self-contained introduction to a state-of-the-art machine learning approach, Ensemble Methods: Foundations and Algorithms shows how these accurate methods are used in real-world tasks. It gives you the necessary groundwork to carry out further research in this evolving field. After presenting background and terminology, the book covers the main algorithms and theories, including Boosting, Bagging, Random Forest, averaging and voting schemes, the Stacking method, mixture of experts, and diversity measures. It also discusses multiclass extension, noise tolerance, error-ambiguity and bias-variance decompositions, and recent progress in information theoretic diversity. Moving on to more advanced topics, the author explains how to achieve better performance through ensemble pruning and how to generate better clustering results by combining multiple clusterings. In addition, he describes developments of ensemble methods in semi-supervised learning, active learning, cost-sensitive learning, class-imbalance learning, and comprehensibility enhancement.
Ensemble learning is the learning paradigm which employs multiple learners to solve one task @cite_23 , and it achieves state-of-the-art performance in many practice applications. In current work, the final classifier generated by CAPO is an ensemble constituting of auxiliary classifiers and the delta function. But, different from conventional ensemble methods, the component classifiers of CAPO are of two kinds and generated in two steps: first, auxiliary classifiers are trained; then a delta function which is designed to correct the decision of auxiliary classifiers is added such that the concerned performance measure is optimized.