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The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
The support vector machine (SVM) is a supervised learning algorithm that finds a maximum-margin linear classifier, often after mapping the data to a high-dimensional feature space via the kernel trick. Recent work has demonstrated that in…
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…
We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under…
It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample…
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…
Kernel-based machine learning algorithms are based on mapping data from the original input feature space to a kernel feature space of higher dimensionality to solve a linear problem in that space. Over the last decade, kernel based…
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…
We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support…
Multi Task Learning (MTL) efficiently leverages useful information contained in multiple related tasks to help improve the generalization performance of all tasks. This article conducts a large dimensional analysis of a simple but, as we…
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a…
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 computational complexity of solving nonlinear support vector machine (SVM) is prohibitive on large-scale data. In particular, this issue becomes very sensitive when the data represents additional difficulties such as highly imbalanced…
Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data,…
The support vector machine (SVM) and minimum Euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high-dimensional data through…
The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions…
The soft-margin support vector machine (SVM) is a ubiquitous tool for prediction of binary-response data. However, the SVM is characterized entirely via a numerical optimization problem, rather than a probability model, and thus does not…
In the last few years, various types of machine learning algorithms, such as Support Vector Machine (SVM), Support Vector Regression (SVR), and Non-negative Matrix Factorization (NMF) have been introduced. The kernel approach is an…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists…