Related papers: High-Dimensional Penalized Bernstein Support Vecto…
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…
The support vector machine (SVM) is a widely used machine learning tool for classification based on statistical learning theory. Given a set of training data, the SVM finds a hyperplane that separates two different classes of data points by…
Support vector machines (SVMs) are powerful supervised learning tools developed to solve classification problems. However, SVMs are likely to perform poorly in the classification of imbalanced data. The rough set theory presents a…
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…
In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix…
The support vector machine (SVM) is a supervised learning algorithm that finds a maximum-margin linear classifier, often after mapping the data to a high-dimensional feature space via the kernel trick. Recent work has demonstrated that in…
In this paper, we study the embedded feature selection problem in linear Support Vector Machines (SVMs), in which a cardinality constraint is employed, leading to an interpretable classification model. The problem is NP-hard due to the…
Support vector machines (SVMs) appeared in the early nineties as optimal margin classifiers in the context of Vapnik's statistical learning theory. Since then SVMs have been successfully applied to real-world data analysis problems, often…
Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved with nonlinear optimization methods. It is generally accepted that second order descent methods are the most robust, fast, and…
We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and…
Binary codes have been widely used in vision problems as a compact feature representation to achieve both space and time advantages. Various methods have been proposed to learn data-dependent hash functions which map a feature vector to a…
Support Vector Machine (SVM) is a state-of-the-art classification method widely used in science and engineering due to its high accuracy, its ability to deal with high dimensional data, and its flexibility in modeling diverse sources of…
The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…
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…
While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…
Feature selection is critical in machine learning to reduce dimensionality and improve model accuracy and efficiency. The exponential growth in feature space dimensionality for modern datasets directly results in ambiguous samples and…
Regularized risk minimization with the binary hinge loss and its variants lies at the heart of many machine learning problems. Bundle methods for regularized risk minimization (BMRM) and the closely related SVMStruct are considered the best…
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…