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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…
Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, Transcranial Doppler ultrasound (TCD) is a noninvasive…
Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…
This article provides a practical introduction to kernel discrepancies, focusing on the Maximum Mean Discrepancy (MMD), the Hilbert-Schmidt Independence Criterion (HSIC), and the Kernel Stein Discrepancy (KSD). Various estimators for these…
In this paper, a novel framework of sparse kernel learning for Support Vector Data Description (SVDD) based anomaly detection is presented. In this work, optimal sparse feature selection for anomaly detection is first modeled as a Mixed…
Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…
We introduce a semi-supervised learning estimator which tends to the first kernel principal component as the number of labelled points vanishes. Our approach is based on the notion of optimal target vector, which is defined as follows.…
We investigate the stochastic gradient descent (SGD) method where the step size lies within a banded region instead of being given by a fixed formula. The optimal convergence rate under mild conditions and large initial step size is proved.…
Generative Adversarial Networks (GANs) have become a widely popular framework for generative modelling of high-dimensional datasets. However their training is well-known to be difficult. This work presents a rigorous statistical analysis of…
Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…
Support Vector Machines are a widely used classification technique. They are computationally efficient and provide excellent predictions even for high-dimensional data. Moreover, Support Vector Machines are very flexible due to the…
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…
This paper proposes the adaptation of Support Vector Data Description (SVDD) to the multiple kernel case (MK-SVDD), based on SimpleMKL. It also introduces a variant called Slim-MK-SVDD that is able to produce a tighter frontier around the…
Stein variational gradient descent (SVGD) is a particle-based inference algorithm that leverages gradient information for efficient approximate inference. In this work, we enhance SVGD by leveraging preconditioning matrices, such as the…
In this paper, we present an adaptation of Newton's method for the optimization of Subspace Support Vector Data Description (S-SVDD). The objective of S-SVDD is to map the original data to a subspace optimized for one-class classification,…
We propose a novel parametric dictionary learning algorithm for line spectral estimation, applicable in both single measurement vector (SMV) and multiple measurement vectors (MMV) scenarios. This algorithm, termed cubic Newtonized K-SVD…
Although support vector machines (SVMs) are theoretically well understood, their underlying optimization problem becomes very expensive, if, for example, hundreds of thousands of samples and a non-linear kernel are considered. Several…
It is well-known that the precision of data, hyperparameters, and internal representations employed in learning systems directly impacts its energy, throughput, and latency. The precision requirements for the training algorithm are also…
Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction…
What enables Stochastic Gradient Descent (SGD) to achieve better generalization than Gradient Descent (GD) in Neural Network training? This question has attracted much attention. In this paper, we study the distribution of the Stochastic…