Related papers: Universal Consistency and Robustness of Localized …

Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems,…

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…

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…

Most metric learning algorithms, as well as Fisher's Discriminant Analysis (FDA), optimize some cost function of different measures of within-and between-class distances. On the other hand, Support Vector Machines(SVMs) and several Multiple…

The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…

We prove a few representer theorems for a localised version of the regularised and multiview support vector machine learning problem introduced by H.Q. Minh, L. Bazzani, and V. Murino, Journal of Machine Learning Research, 17(2016) 1-72,…

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…

Support Vector Machine (SVM) is a robust machine learning algorithm with broad applications in classification, regression, and outlier detection. SVM requires tuning the regularization parameter (RP) which controls the model capacity and…

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.…

The fundamental goal of self-supervised learning (SSL) is to produce useful representations of data without access to any labels for classifying the data. Modern methods in SSL, which form representations based on known or constructed…

When neural circuits learn to perform a task, it is often the case that there are many sets of synaptic connections that are consistent with the task. However, only a small number of possible solutions are robust to noise in the input and…

In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…

The support vector clustering algorithm is a well-known clustering algorithm based on support vector machines using Gaussian or polynomial kernels. The classical support vector clustering algorithm works well in general, but its performance…

The support vector machine (SVM) is a widely used machine learning tool for classification based on statistical learning theory. Given a set of training data, the SVM finds a hyperplane that separates two different classes of data points by…

Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

This paper analyzes a new regularized learning scheme for high dimensional partially linear support vector machine. The proposed approach consists of an empirical risk and the Lasso-type penalty for linear part, as well as the standard…

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…

Anomaly detection is defined as the problem of finding data points that do not follow the patterns of the majority. Among the various proposed methods for solving this problem, classification-based methods, including one-class Support…

Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…