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The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…

Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve…

The Gaussian kernel and its derivatives have already been employed for Convolutional Neural Networks in several previous works. Most of these papers proposed to compute filters by linearly combining one or several bases of fixed or slightly…

In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil…

The growing demand for structural health monitoring has driven increasing interest in high-precision motion measurement, as structural information derived from extracted motions can effectively reflect the current condition of the…

The Weisfeiler-Lehman graph kernels are among the most prevalent graph kernels due to their remarkable time complexity and predictive performance. Their key concept is based on an implicit comparison of neighborhood representing trees with…

Random walk kernels have been introduced in seminal work on graph learning and were later largely superseded by kernels based on the Weisfeiler-Leman test for graph isomorphism. We give a unified view on both classes of graph kernels. We…

In this work, we apply Convolutional Neural Networks (CNNs) to detect gravitational wave (GW) signals of compact binary coalescences, using single-interferometer data from LIGO detectors. As novel contribution, we adopted a resampling…

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…

A device called a 'Gaussian Boson Sampler' has initially been proposed as a near-term demonstration of classically intractable quantum computation. As recently shown, it can also be used to decide whether two graphs are isomorphic. Based on…

This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in…

Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate…

The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of…

Based on a proposed classical explanation, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment.…

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…

Most recent semantic segmentation methods train deep convolutional neural networks with fully annotated masks requiring pixel-accuracy for good quality training. Common weakly-supervised approaches generate full masks from partial input…

Convolutional Neural Networks (CNNs) are generally prone to noise interruptions, i.e., small image noise can cause drastic changes in the output. To suppress the noise effect to the final predication, we enhance CNNs by replacing…

Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…

We report on the construction of a deep convolutional neural network that can reproduce the sensitivity of a matched-filtering search for binary black hole gravitational-wave signals. The standard method for the detection of well modeled…