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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…

A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with…

Classification is one of the main areas of pattern recognition research, and within it, Support Vector Machine (SVM) is one of the most popular methods outside of field of deep learning -- and a de-facto reference for many Machine Learning…

We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions…

Logistic models are commonly used for binary classification tasks. The success of such models has often been attributed to their connection to maximum-likelihood estimators. It has been shown that gradient descent algorithm, when applied on…

Recent advance on linear support vector machine with the 0-1 soft margin loss ($L_{0/1}$-SVM) shows that the 0-1 loss problem can be solved directly. However, its theoretical and algorithmic requirements restrict us extending the linear…

Let X be a data matrix of rank \rho, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension…

The imminent advent of very large-scale optical sky surveys, such as Euclid and LSST, makes it important to find efficient ways of discovering rare objects such as strong gravitational lens systems, where a background object is multiply…

In this paper, we study the hard and soft support vector regression techniques applied to a set of $n$ linear measurements of the form $y_i=\boldsymbol{\beta}_\star^{T}{\bf x}_i +n_i$ where $\boldsymbol{\beta}_\star$ is an unknown vector,…

Gaussian mixture models (GMM) and support vector machines (SVM) are introduced to classify faults in a population of cylindrical shells. The proposed procedures are tested on a population of 20 cylindrical shells and their performance is…

Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of…

Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…

A novel linear classification method that possesses the merits of both the Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is proposed in this article. The proposed Distance-weighted Support Vector Machine method…

Support vector machines (SVMs) are a standard method in the machine learning toolbox, in particular for tabular data. Non-linear kernel SVMs often deliver highly accurate predictors, however, at the cost of long training times. That problem…

Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes. Motivated by…

This paper presents a review on methods for class-imbalanced learning with the Support Vector Machine (SVM) and its variants. We first explain the structure of SVM and its variants and discuss their inefficiency in learning with…

In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In…

Most supervised learning models are trained for full automation. However, their predictions are sometimes worse than those by human experts on some specific instances. Motivated by this empirical observation, our goal is to design…

Most data in genome-wide phylogenetic analysis (phylogenomics) is essentially multidimensional, posing a major challenge to human comprehension and computational analysis. Also, we can not directly apply statistical learning models in data…

For binary classification we establish learning rates up to the order of $n^{-1}$ for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions:…