相关论文: Learning with Smooth Hinge Losses

The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as…

Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which…

Support Vector Machines (SVMs) based on hinge loss have been extensively discussed and applied to various binary classification tasks. These SVMs achieve a balance between margin maximization and the minimization of slack due to outliers.…

Loss function plays a vital role in supervised learning frameworks. The selection of the appropriate loss function holds the potential to have a substantial impact on the proficiency attained by the acquired model. The training of…

A smoothing algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an…

Over the past two decades, support vector machine (SVM) has become a popular supervised machine learning model, and plenty of distinct algorithms are designed separately based on different KKT conditions of the SVM model for…

We propose a new convex loss for Support Vector Machines, both for the binary classification and for the regression models. Therefore, we show the mathematical derivation of the dual problems and we experiment with them on several small…

Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new…

Sparsity-inducing penalties are useful tools to design multiclass support vector machines (SVMs). In this paper, we propose a convex optimization approach for efficiently and exactly solving the multiclass SVM learning problem involving a…

Support vector machine is an important and fundamental technique in machine learning. In this paper, we apply a semismooth Newton method to solve two typical SVM models: the L2-loss SVC model and the \epsilon-L2-loss SVR model. The…

A new algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an important…

The binomial deviance and the SVM hinge loss functions are two of the most widely used loss functions in machine learning. While there are many similarities between them, they also have their own strengths when dealing with different types…

Twin support vector machine (TSVM), a variant of support vector machine (SVM), has garnered significant attention due to its $3/4$ times lower computational complexity compared to SVM. However, due to the utilization of the hinge loss…

Distance/Similarity learning is a fundamental problem in machine learning. For example, kNN classifier or clustering methods are based on a distance/similarity measure. Metric learning algorithms enhance the efficiency of these methods by…

This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…

Support vector machine (SVM) has proved to be a successful approach for machine learning. Two typical SVM models are the L1-loss model for support vector classification (SVC) and $\epsilon$-L1-loss model for support vector regression (SVR).…

The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$…

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and…

The support vector machines (SVM) is a powerful classifier used for binary classification to improve the prediction accuracy. However, the non-differentiability of the SVM hinge loss function can lead to computational difficulties in high…

The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized…