244,755 research outputs found
Statistical Mechanics of Soft Margin Classifiers
We study the typical learning properties of the recently introduced Soft
Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the
tools of Statistical Mechanics. We derive analytically the behaviour of the
learning curves in the regime of very large training sets. We obtain
exponential and power laws for the decay of the generalization error towards
the asymptotic value, depending on the task and on general characteristics of
the distribution of stabilities of the patterns to be learned. The optimal
learning curves of the SMCs, which give the minimal generalization error, are
obtained by tuning the coefficient controlling the trade-off between the error
and the regularization terms in the cost function. If the task is realizable by
the SMC, the optimal performance is better than that of a hard margin Support
Vector Machine and is very close to that of a Bayesian classifier.Comment: 26 pages, 12 figures, submitted to Physical Review
Exploiting diversity for optimizing margin distribution in ensemble learning
Margin distribution is acknowledged as an important factor for improving the generalization performance of classifiers. In this paper, we propose a novel ensemble learning algorithm named Double Rotation Margin Forest (DRMF), that aims to improve the margin distribution of the combined system over the training set. We utilise random rotation to produce diverse base classifiers, and optimize the margin distribution to exploit the diversity for producing an optimal ensemble. We demonstrate that diverse base classifiers are beneficial in deriving large-margin ensembles, and that therefore our proposed technique will lead to good generalization performance. We examine our method on an extensive set of benchmark classification tasks. The experimental results confirm that DRMF outperforms other classical ensemble algorithms such as Bagging, AdaBoostM1 and Rotation Forest. The success of DRMF is explained from the viewpoints of margin distribution and diversity
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