Related papers: GBSVR: Granular Ball Support Vector Regression

Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great…

Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms…

Support vector machines (SVMs) appeared in the early nineties as optimal margin classifiers in the context of Vapnik's statistical learning theory. Since then SVMs have been successfully applied to real-world data analysis problems, often…

Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…

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…

Recently, 3D Gaussian Splatting (3DGS) has attracted widespread attention due to its high-quality rendering, and ultra-fast training and rendering speed. However, due to the unstructured and irregular nature of Gaussian point clouds, it is…

Reconstructing 3D fetal MR volumes from motion-corrupted stacks of 2D slices is a crucial and challenging task. Conventional slice-to-volume reconstruction (SVR) methods are time-consuming and require multiple orthogonal stacks for…

In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…

This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…

Variable selection has become a pivotal choice in data analyses that impacts subsequent inference and prediction. In linear models, variable selection using Second-Generation P-Values (SGPV) has been shown to be as good as any other…

In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…

Support vector regression (SVR) has garnered significant popularity over the past two decades owing to its wide range of applications across various fields. Despite its versatility, SVR encounters challenges when confronted with outliers…

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…

Support vector machine (SVM) is a powerful classification method that has achieved great success in many fields. Since its performance can be seriously impaired by redundant covariates, model selection techniques are widely used for SVM…

The support vector machine (SVM) is a widely used method for classification. Although many efforts have been devoted to develop efficient solvers, it remains challenging to apply SVM to large-scale problems. A nice property of SVM is that…

Capturing semantic consistency among nodes is crucial for effective graph representation learning. Existing approaches typically rely on $k$-nearest neighbors ($k$NN) or other node-level full search algorithms (FSA) to mine semantic…

Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…

Residual bootstrap is a classical method for statistical inference in regression settings. With massive data sets becoming increasingly common, there is a demand for computationally efficient alternatives to residual bootstrap. We propose a…

Bayesian computation plays an important role in modern machine learning and statistics to reason about uncertainty. A key computational challenge in Bayesian inference is to develop efficient techniques to approximate, or draw samples from…

The purpose of this report is in examining the generalization performance of Support Vector Machines (SVM) as a tool for pattern recognition and object classification. The work is motivated by the growing popularity of the method that is…