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Quantum machine learning (QML) has witnessed immense progress recently, with quantum support vector machines (QSVMs) emerging as a promising model. This paper focuses on the two existing QSVM methods: quantum kernel SVM (QK-SVM) and quantum…
The support vector machine (SVM) is an important class of learning machines for function approach, pattern recognition, and time-serious prediction, etc. It maps samples into the feature space by so-called support vectors of selected…
In this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings. We show that the hard-margin linear SVM holds a consistency property in which misclassification rates…
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…
Tackling pattern recognition problems in areas such as computer vision, bioinformatics, speech or text recognition is often done best by taking into account task-specific statistical relations between output variables. In structured…
In the domain of machine learning, least square twin support vector machine (LSTSVM) stands out as one of the state-of-the-art models. However, LSTSVM suffers from sensitivity to noise and outliers, overlooking the SRM principle and…
Using methods of Statistical Physics, we investigate the generalization performance of support vector machines (SVMs), which have been recently introduced as a general alternative to neural networks. For nonlinear classification rules, the…
The huge amount of available data nowadays is a challenge for kernel-based machine learning algorithms like SVMs with respect to runtime and storage capacities. Local approaches might help to relieve these issues and to improve statistical…
Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…
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…
Twin support vector machine (TSVM) is a very classical and practical classifier for pattern classification. However, the traditional TSVM has two limitations. Firstly, it uses the L_2-norm distance metric that leads to its sensitivity to…
The support vector machine (SVM) algorithm is well known to the computer learning community for its very good practical results. The goal of the present paper is to study this algorithm from a statistical perspective, using tools of…
For the binary classification problem, a novel nonlinear kernel-free quadratic hyper-surface support vector machine with 0-1 loss function (QSSVM$_{0/1}$) is proposed. Specifically, the task of QSSVM$_{0/1}$ is to seek a quadratic…
Typically, nonlinear Support Vector Machines (SVMs) produce significantly higher classification quality when compared to linear ones but, at the same time, their computational complexity is prohibitive for large-scale datasets: this…
Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image…
High dimension, low sample size (HDLSS) problems are numerous among real-world applications of machine learning. From medical images to text processing, traditional machine learning algorithms are usually unsuccessful in learning the best…
We address the problem of model selection for Support Vector Machine (SVM) classification. For fixed functional form of the kernel, model selection amounts to tuning kernel parameters and the slack penalty coefficient $C$. We begin by…
We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…
Support Vector Machines (SVMs) are well-established Machine Learning (ML) algorithms. They rely on the fact that i) linear learning can be formalized as a well-posed optimization problem; ii) non-linear learning can be brought into linear…
We present a new approach to obtaining photometric redshifts using a kernel learning technique called Support Vector Machines (SVMs). Unlike traditional spectral energy distribution fitting, this technique requires a large and…