Related papers: Analysis and Extension of Arc-Cosine Kernels for L…

In this paper, we define and study a nested family of reproducing kernel Hilbert spaces of vector fields that is indexed by a range of scales, from which we construct a reproducing kernel Hilbert space of scale-dependent vector fields. We…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…

The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also introduce two additional reproducing kernel Hilbert spaces…

Prominently used in support vector machines and logistic regressions, kernel functions (kernels) can implicitly map data points into high dimensional spaces and make it easier to learn complex decision boundaries. In this work, by replacing…

The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its…

Segmentation of certain hollow organs, such as the bladder, is especially hard to automate due to their complex geometry, vague intensity gradients in the soft tissues, and a tedious manual process of the data annotation routine. Yet,…

Applying kernel methods to matchings is challenging due to their discrete, non-Euclidean nature. In this paper, we develop a principled framework for constructing geometric kernels that respect the natural geometry of the space of…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

We define a family of kernels for mixed continuous/discrete hierarchical parameter spaces and show that they are positive definite.

Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In…

Recently, a unified framework for adaptive kernel based signal processing of complex data was presented by the authors, which, besides offering techniques to map the input data to complex Reproducing Kernel Hilbert Spaces, developed a…

The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their…

The paper is an investigation of the analytic properties of a new class of special functions that appear in the kernels of a class of integral operators underlying the dynamics of matter relaxation processes in attractive fields. These…

We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…

The importance of wild video based image set recognition is becoming monotonically increasing. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a…

Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…

The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…

This article studies sufficient conditions on families of approximating kernels which provide $N$--term approximation errors from an associated nonlinear approximation space which match the best known orders of $N$--term wavelet expansion.…