Related papers: A Quadratic Loss Multi-Class SVM
One of the limiting factors of using support vector machines (SVMs) in large scale applications are their super-linear computational requirements in terms of the number of training samples. To address this issue, several approaches that…
The Vapnik-Chervonenkis (VC) dimension measures the complexity of a learning machine, and a low VC dimension leads to good generalization. The recently proposed Minimal Complexity Machine (MCM) learns a hyperplane classifier by minimizing…
A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…
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…
A nonlinear kernel-free soft quadratic surface support vector machine model with 0-1 loss function ($L_{0/1}$-SQSSVM) is proposed for binary classification problems, which is non-convex discontinuous. We are devoted to establishing the…
The field of Astronomy requires the collection and assimilation of vast volumes of data. The data handling and processing problem has become severe as the sheer volume of data produced by scientific instruments each night grows…
We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization…
Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…
Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and…
In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for…
Aerodynamics plays an important role in aviation industry and aircraft design. Detecting and minimizing the phenomenon of flow separation from scattered pressure data on airfoil is critical for ensuring stable and efficient aviation.…
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…
Classification is often the first problem described in introductory machine learning classes. Generalization guarantees of classification have historically been offered by Vapnik-Chervonenkis theory. Yet those guarantees are based on…
In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…
Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which…
Support vector machines (SVMs) are widely used machine learning models (e.g., in remote sensing), with formulations for both classification and regression tasks. In the last years, with the advent of working quantum annealers, hybrid SVM…
The growing size of modern data brings many new challenges to existing statistical inference methodologies and theories, and calls for the development of distributed inferential approaches. This paper studies distributed inference for…
Margin has played an important role on the design and analysis of learning algorithms during the past years, mostly working with the maximization of the minimum margin. Recent years have witnessed the increasing empirical studies on the…