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, ...

The midline diastema is a space (or gap) between the maxillary central incisors . The space can be a normal growth characteristic during the primary and mixed dentition and generally is closed by the time the maxillary canines erupt. Researchers and clinicians now believe that multiple factors may contribute to a midline space including abnormal frenum, midline bony clefts ,oral habits, soft ti...

In a classification problem, hard margin SVMs tend to minimize the generalization error by maximizing the margin. Regularization is obtained with soft margin SVMs which improve performances by relaxing the constraints on the margin maximization. This article shows that comparable performances can be obtained in the linearly separable case with the Ho–Kashyap learning rule associated to early st...

In a classification problem, hard margin SVMs tend to minimize the generalization error by maximizing the margin. Regularization is obtained with soft margin SVMs which improve performances by relaxing the constraints on the margin maximization. This article shows that comparable performances can be obtained in the linearly separable case with the Ho–Kashyap learning rule associated to early st...

BACKGROUND & OBJECTIVE Peripheral tumor growth pattern plays an important role in the local recurrence and metastases of soft tissue sarcoma. This study was to determine the peripheral growth pattern of soft tissue sarcoma by magnetic resonance imaging (MRI), explore its correlation to histological grade, and assess biological features of soft tissue sarcoma before operation. METHODS MRI was ...

One of the well known risks of large margin training methods, such as boosting and support vector machines (SVMs), is their sensitivity to outliers. These risks are normally mitigated by using a soft margin criterion, such as hinge loss, to reduce outlier sensitivity. In this paper, we present a more direct approach that explicitly incorporates outlier suppression in the training process. In pa...

In the design of support vector machines an important step is to select the optimal hyperparameters. One of the most used estimators of the performance is the Radius-Margin bound. Some modifications of this bound have been made to adapt it to soft margin problems, giving a convex optimization problem for the L2 soft margin formulation. However, it is still interesting to consider the L1 case du...

Supervised machine learning is an important building block for many applications that involve data processing and decision making. Good classifiers are trained to produce accurate predictions on a training set while also generalizing well to unseen data. To this end, Bayes-PointMachines (bpm) were proposed in the past as a generalization of margin maximizing classifiers, such as Support-Vector-...