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In this paper, we correct an upper bound, presented in~\cite{hs-11}, on the generalisation error of classifiers learned through multiple kernel learning. The bound in~\cite{hs-11} uses Rademacher complexity and has an\emph{additive}…

This paper presents several novel generalization bounds for the problem of learning kernels based on the analysis of the Rademacher complexity of the corresponding hypothesis sets. Our bound for learning kernels with a convex combination of…

Complex classifiers may exhibit "embarassing" failures in cases where humans can easily provide a justified classification. Avoiding such failures is obviously of key importance. In this work, we focus on one such setting, where a label is…

One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the…

This paper proposes a simple yet powerful ensemble classifier, called Random Hyperboxes, constructed from individual hyperbox-based classifiers trained on the random subsets of sample and feature spaces of the training set. We also show a…

This paper proposes a systematic framework to design a classification model that yields a classifier which optimizes a utility function based on prior knowledge. Specifically, as the data size grows, we prove that the produced classifier…

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…

In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…

We provide new general kernel selection rules thanks to penalized least-squares criteria. We derive optimal oracle inequalities using adequate concentration tools. We also investigate the problem of minimal penalty as described in [BM07].

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

Learning classifiers that are robust to adversarial examples has received a great deal of recent attention. A major drawback of the standard robust learning framework is there is an artificial robustness radius $r$ that applies to all…

Improving the performance of classifiers is the realm of feature mapping, prototype selection, and kernel function transformations; these techniques aim for reducing the complexity, and also, improving the accuracy of models. In particular,…

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…

The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along…

In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel…

Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…