Related papers: On $\ell_p$-Support Vector Machines and Multidimen…
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…
We study a variant of the median problem for a collection of point sets in high dimensions. This generalizes the geometric median as well as the (probabilistic) smallest enclosing ball (pSEB) problems. Our main objective and motivation is…
Support Vector Machines (SVMs) are popular tools for data mining tasks such as classification, regression, and density estimation. However, original SVM (C-SVM) only considers local information of data points on or over the margin.…
Support vector machines (SVMs) are popular learning algorithms to deal with binary classification problems. They traditionally assume equal misclassification costs for each class; however, real-world problems may have an uneven class…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, 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…
The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known…
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…
Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…
Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…
Kernel matrix-vector product is ubiquitous in many science and engineering applications. However, a naive method requires $O(N^2)$ operations, which becomes prohibitive for large-scale problems. We introduce a parallel method that provably…
In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…
Large Language Models (LLMs) enable a new form of digital experimentation where treatments combine human and model-generated content in increasingly sophisticated ways. The main methodological challenge in this setting is representing these…
The parameters of support vector machines (SVMs) such as the penalty parameter and the kernel parameters have a great impact on the classification accuracy and the complexity of the SVM model. Therefore, the model selection in SVM involves…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
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…
With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine…
The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…
Support Vector Machines (SVM) have gathered significant acclaim as classifiers due to their successful implementation of Statistical Learning Theory. However, in the context of multiclass and multilabel settings, the reliance on…