Related papers: Smoothed Hinge Loss and $\ell^{1}$ Support Vector …
We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net…
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…
Stochastic First-Order (SFO) methods have been a cornerstone in addressing a broad spectrum of modern machine learning (ML) challenges. However, their efficacy is increasingly questioned, especially in large-scale applications where…
Support vector machines (SVMs) are popular learning algorithms to deal with binary classification problems. They traditionally assume equal misclassification costs for each class; however, real-world problems may have an uneven class…
In this article we consider the problem of testing, for two finite sets of points in the Euclidean space, if their convex hulls are disjoint and computing an optimal supporting hyperplane if so. This is a fundamental problem of…
Support vector machine (SVM) is a popular classifier known for accuracy, flexibility, and robustness. However, its intensive computation has hindered its application to large-scale datasets. In this paper, we propose a new optimal leverage…
Support Vector Machines (SVM) with $\ell_1$ penalty became a standard tool in analysis of highdimensional classification problems with sparsity constraints in many applications including bioinformatics and signal processing. Although SVM…
The sequential minimal optimization (SMO) algorithm and variants thereof are the de facto standard method for solving large quadratic programs for support vector machine (SVM) training. In this paper we propose a simple yet powerful…
Support vector machine (SVM) is a powerful classification method that has achieved great success in many fields. Since its performance can be seriously impaired by redundant covariates, model selection techniques are widely used for SVM…
In modern classification tasks, the number of labels is getting larger and larger, as is the size of the datasets encountered in practice. As the number of classes increases, class ambiguity and class imbalance become more and more…
In this work we consider the stochastic minimization of nonsmooth convex loss functions, a central problem in machine learning. We propose a novel algorithm called Accelerated Nonsmooth Stochastic Gradient Descent (ANSGD), which exploits…
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…
We consider a linear regression problem in a high dimensional setting where the number of covariates $p$ can be much larger than the sample size $n$. In such a situation, one often assumes sparsity of the regression vector, \textit i.e.,…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…
We propose $\ell_1$ norm regularized quadratic surface support vector machine models for binary classification in supervised learning. We establish their desired theoretical properties, including the existence and uniqueness of the optimal…
In this paper, a white-Box support vector machine (SVM) framework and its swarm-based optimization is presented for supervision of toothed milling cutter through characterization of real-time spindle vibrations. The anomalous moments of…
Localized support vector machines solve SVMs on many spatially defined small chunks and one of their main characteristics besides the computational benefit compared to global SVMs is the freedom of choosing arbitrary kernel and…
We investigate convexification for convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step…
The logistic loss function is often advocated in machine learning and statistics as a smooth and strictly convex surrogate for the 0-1 loss. In this paper we investigate the question of whether these smoothness and convexity properties make…