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Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of relevant features), and robustness. For linear models, it is…

In this article, we propose a new Support Vector Machine (SVM) training algorithm based on distributed MapReduce technique. In literature, there are a lots of research that shows us SVM has highest generalization property among…

The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…

In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…

The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions…

The parameters of support vector machines (SVMs) such as the penalty parameter and the kernel parameters have a great impact on the classification accuracy and the complexity of the SVM model. Therefore, the model selection in SVM involves…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

We propose a novel criterion for support vector machine learning: maximizing the margin in the input space, not in the feature (Hilbert) space. This criterion is a discriminative version of the principal curve proposed by Hastie et al. The…

Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…

This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the…

Support vector machine (SVM), is a popular kernel method for data classification that demonstrated its efficiency for a large range of practical applications. The method suffers, however, from some weaknesses including; time processing,…

Support Vector Machine (SVM) is an effective model for many classification problems. However, SVM needs the solution of a quadratic program which require specialized code. In addition, SVM has many parameters, which affects the performance…

The support vector machine (SVM) is one of the most successful learning methods for solving classification problems. Despite its popularity, SVM has a serious drawback, that is sensitivity to outliers in training samples. The penalty on…

We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

Ridge regularized linear models (RRLMs), such as ridge regression and the SVM, are a popular group of methods that are used in conjunction with coefficient hypothesis testing to discover explanatory variables with a significant multivariate…

The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…

One of the limiting factors of using support vector machines (SVMs) in large scale applications are their super-linear computational requirements in terms of the number of training samples. To address this issue, several approaches that…

We review the concept of support vector machines (SVMs) and discuss examples of their use. One of the benefits of SVM algorithms, compared with neural networks and decision trees is that they can be less susceptible to over fitting than…

Popular methods for finding regularized solutions to inverse problems include sparsity promoting $\ell_1$ regularization techniques, one in particular which is the well known total variation (TV) regularization. More recently, several…