Related papers: An Equivalence between the Lasso and Support Vecto…
Estimating the importance of variables is an essential task in modern machine learning. This help to evaluate the goodness of a feature in a given model. Several techniques for estimating the importance of variables have been developed…
Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical…
Model selection is difficult to analyse yet theoretically and empirically important, especially for high-dimensional data analysis. Recently the least absolute shrinkage and selection operator (Lasso) has been applied in the statistical and…
In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We show that the problem of generalized support vector machine is equivalent to the problem of…
Support Vector Machines (SVMs) are among the most popular and the best performing classification algorithms. Various approaches have been proposed to reduce the high computation and memory cost when training and predicting based on…
Support Vector Machines (SVMs) are an important tool for performing classification on scattered data, where one usually has to deal with many data points in high-dimensional spaces. We propose solving SVMs in primal form using feature maps…
In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods…
We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…
Quantum support vector machines have the potential to achieve a quantum speedup for solving certain machine learning problems. The key challenge for doing so is finding good quantum kernels for a given data set -- a task called kernel…
The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…
We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is…
Support vector machine algorithms are considered essential for the implementation of automation in a radio access network. Specifically, they are critical in the prediction of the quality of user experience for video streaming based on…
We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…
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…
This chapter describes componentwise Least Squares Support Vector Machines (LS-SVMs) for the estimation of additive models consisting of a sum of nonlinear components. The primal-dual derivations characterizing LS-SVMs for the estimation of…
The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…
Machine learning algorithms must be able to efficiently cope with massive data sets. Therefore, they have to scale well on any modern system and be able to exploit the computing power of accelerators independent of their vendor. In the…
Neural support vector machines (NSVMs) allow for the incorporation of domain knowledge in the design of the model architecture. In this article we introduce a set of training algorithms for NSVMs that leverage the Pegasos algorithm and…
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…