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We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the…
Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…
Multiple kernel learning (MKL) method is generally believed to perform better than single kernel method. However, some empirical studies show that this is not always true: the combination of multiple kernels may even yield an even worse…
We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study (cf. [26]), it was shown that bivariate spline functions of…
This paper introduces a directional multiscale algorithm for the two dimensional $N$-body problem of the Helmholtz kernel with applications to high frequency scattering. The algorithm follows the approach in [Engquist and Ying, SIAM Journal…
We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
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…
We consider the two-group classification problem and propose a kernel classifier based on the optimal scoring framework. Unlike previous approaches, we provide theoretical guarantees on the expected risk consistency of the method. We also…
In this paper, we address the problem of reconstructing coverage maps from path-loss measurements in cellular networks. We propose and evaluate two kernel-based adaptive online algorithms as an alternative to typical offline methods. The…
In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…
This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…
Machine learning methods usually depend on internal parameters -- so called hyperparameters -- that need to be optimized for best performance. Such optimization poses a burden on machine learning practitioners, requiring expert knowledge,…
We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…