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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…
Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be…
Support Vector Machine (SVM) has been one of the most successful machine learning techniques for binary classification problems. The key idea is to maximize the margin from the data to the hyperplane subject to correct classification on…
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…
Constrained combinatorial optimization problems are frequently reformulated as quadratic unconstrained binary optimization (QUBO) models in order to leverage emerging quantum optimization algorithms such as the Variational Quantum…
We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on…
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…
Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…
This paper addresses feature subset selection for Support Vector Machines (SVMs) based on the cross-validation criterion. Unlike statistical criteria such as the Akaike information criterion (AIC) and the Bayesian information criterion…
We describe an apparatus for subgradient-following of the optimum of convex problems with variational penalties. In this setting, we receive a sequence $y_i,\ldots,y_n$ and seek a smooth sequence $x_1,\ldots,x_n$. The smooth sequence needs…
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
Support vector machine (SVM), is a popular kernel method for data classification that demonstrated its efficiency for a large range of practical applications. The method suffers, however, from some weaknesses including; time processing,…
The support vector machines (SVM) is one of the most widely used and practical optimization based classification models in machine learning because of its interpretability and flexibility to produce high quality results. However, the big…
Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vector Machines (SVMs). Linear and kernel SVMs have been among…
We present multiplicative updates for solving hard and soft margin support vector machines (SVM) with non-negative kernels. They follow as a natural extension of the updates for non-negative matrix factorization. No additional param- eter…
Support vector machines (SVM) can classify data sets along highly non-linear decision boundaries because of the kernel-trick. This expressiveness comes at a price: During test-time, the SVM classifier needs to compute the kernel…
This paper examines the application of a Quantum Support Vector Machine (QSVM) for radarbased aerial target classification using micro-Doppler signatures. Classical features are extracted and reduced via Principal Component Analysis (PCA)…
Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a…
Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis…