Related papers: Fast rates for support vector machines using Gauss…

We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do…

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to…

The soft-margin support vector machine (SVM) is a ubiquitous tool for prediction of binary-response data. However, the SVM is characterized entirely via a numerical optimization problem, rather than a probability model, and thus does not…

Support vector machines (SVMs) are widely used and constitute one of the best examined and used machine learning models for two-class classification. Classification in SVM is based on a score procedure, yielding a deterministic…

Support vector machine modeling is a new approach in machine learning for classification showing good performance on forecasting problems of small samples and high dimensions. Later, it promoted to Support Vector Regression (SVR) for…

In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…

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…

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…

We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead…

In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support…

For the binary classification problem, a novel nonlinear kernel-free quadratic hyper-surface support vector machine with 0-1 loss function (QSSVM$_{0/1}$) is proposed. Specifically, the task of QSSVM$_{0/1}$ is to seek a quadratic…

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…

In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s \in [0,\infty]$) and the compositional assumption. This assumption requires the conditional class probability…

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

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 $p$…

We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that support vector machines (SVMs) using Gaussian…

Limiting the model size of a kernel support vector machine to a pre-defined budget is a well-established technique that allows to scale SVM learning and prediction to large-scale data. Its core addition to simple stochastic gradient…

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…

Support vector data description (SVDD) is a machine learning technique that is used for single-class classification and outlier detection. The idea of SVDD is to find a set of support vectors that defines a boundary around data. When…

Recent work in metric learning has significantly improved the state-of-the-art in k-nearest neighbor classification. Support vector machines (SVM), particularly with RBF kernels, are amongst the most popular classification algorithms that…