We examine a network of learners which address the same classification task but must learn from different data sets. The learners can share a limited portion of their data sets so as to preserve the network load. We introduce DELCO (standing for Decentralized Ensemble Learning with COpulas), a new approach in which the shared data and the trained models are sent to a central machine that allows to build an ensemble of classifiers. The proposed method aggregates the base classifiers using a probabilistic model relying on Gaussian copulas. Experiments on logistic regressor ensembles demonstrate competing accuracy and increased robustness as compared to gold standard approaches. A companion python implementation can be downloaded at https: github.com john-klein DELCO
The ensemble method introduced in this article for the purpose of decentralized learning shares a similar probabilistic framework with the Bayesian approach by Kim and Ghahramani @cite_12 addressing classifier combination. Consequently, we detail this framework and highlight the differences between their approach and ours. Before that, let us formally define what a classification task is about and briefly recall other popular ensemble methods.
@cite_12
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Ensemble methods are learning algorithms that construct a set of classifiers and then classify new data points by taking a (weighted) vote of their predictions. The original ensemble method is Bayesian averaging, but more recent algorithms include error-correcting output coding, Bagging, and boosting. This paper reviews these methods and explains why ensembles can often perform better than any single classifier. Some previous studies comparing ensemble methods are reviewed, and some new experiments are presented to uncover the reasons that Adaboost does not overfit rapidly. 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. Classifier learning with data-sets that suffer from imbalanced class distributions is a challenging problem in data mining community. This issue occurs when the number of examples that represent one class is much lower than the ones of the other classes. Its presence in many real-world applications has brought along a growth of attention from researchers. In machine learning, the ensemble of classifiers are known to increase the accuracy of single classifiers by combining several of them, but neither of these learning techniques alone solve the class imbalance problem, to deal with this issue the ensemble learning algorithms have to be designed specifically. In this paper, our aim is to review the state of the art on ensemble techniques in the framework of imbalanced data-sets, with focus on two-class problems. We propose a taxonomy for ensemble-based methods to address the class imbalance where each proposal can be categorized depending on the inner ensemble methodology in which it is based. In addition, we develop a thorough empirical comparison by the consideration of the most significant published approaches, within the families of the taxonomy proposed, to show whether any of them makes a difference. This comparison has shown the good behavior of the simplest approaches which combine random undersampling techniques with bagging or boosting ensembles. In addition, the positive synergy between sampling techniques and bagging has stood out. Furthermore, our results show empirically that ensemble-based algorithms are worthwhile since they outperform the mere use of preprocessing techniques before learning the classifier, therefore justifying the increase of complexity by means of a significant enhancement of the results. Several pruning strategies that can be used to reduce the size and increase the accuracy of bagging ensembles are analyzed. These heuristics select subsets of complementary classifiers that, when combined, can perform better than the whole ensemble. The pruning methods investigated are based on modifying the order of aggregation of classifiers in the ensemble. In the original bagging algorithm, the order of aggregation is left unspecified. When this order is random, the generalization error typically decreases as the number of classifiers in the ensemble increases. If an appropriate ordering for the aggregation process is devised, the generalization error reaches a minimum at intermediate numbers of classifiers. This minimum lies below the asymptotic error of bagging. Pruned ensembles are obtained by retaining a fraction of the classifiers in the ordered ensemble. The performance of these pruned ensembles is evaluated in several benchmark classification tasks under different training conditions. The results of this empirical investigation show that ordered aggregation can be used for the efficient generation of pruned ensembles that are competitive, in terms of performance and robustness of classification, with computationally more costly methods that directly select optimal or near-optimal subensembles.