Related papers: On $\ell_p$-Support Vector Machines and Multidimen…
In this work we present a quadratic programming approximation of the Semi-Supervised Support Vector Machine (S3VM) problem, namely approximate QP-S3VM, that can be efficiently solved using off the shelf optimization packages. We prove that…
Computing a consensus object from a set of given objects is a core problem in machine learning and pattern recognition. One popular approach is to formulate it as an optimization problem using the generalized median. Previous methods like…
In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of $\ell^p$ regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that…
Support Vector Machine (SVM) is an effective model for many classification problems. However, SVM needs the solution of a quadratic program which require specialized code. In addition, SVM has many parameters, which affects the performance…
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…
This work presents a fully quantum approach to support vector machine (SVM) learning by integrating gate-based quantum kernel methods with quantum annealing-based optimization. We explore the construction of quantum kernels using various…
We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entrywise $\ell_p$-approximation error, for any $p \geq 1$; the case $p = 2$ is the classical SVD problem. We obtain the first provably good…
Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the…
In this paper, we evaluate the performance of various parallel optimization methods for Kernel Support Vector Machines on multicore CPUs and GPUs. In particular, we provide the first comparison of algorithms with explicit and implicit…
We introduce the anti-profile Support Vector Machine (apSVM) as a novel algorithm to address the anomaly classification problem, an extension of anomaly detection where the goal is to distinguish data samples from a number of anomalous and…
In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimization problems in Hilbert spaces. Then, we generalize the…
In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…
We review the concept of Support Vector Machines (SVMs) and discuss examples of their use in a number of scenarios. Several SVM implementations have been used in HEP and we exemplify this algorithm using the Toolkit for Multivariate…
We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization…
Recent studies indicate that kernel machines can often perform similarly or better than deep neural networks (DNNs) on small datasets. The interest in kernel machines has been additionally bolstered by the discovery of their equivalence to…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
We introduce a proximal version of dual coordinate ascent method. We demonstrate how the derived algorithmic framework can be used for numerous regularized loss minimization problems, including $\ell_1$ regularization and structured output…
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…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…
This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…