Related papers: Positive Definite Multi-Kernels for Scattered Data…
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…
In this paper we investigate the class of invariant positive definite kernels on the free semigroup on N generators. We provide a combinatorial description of the positivity of the kernel in terms of Dyck paths and then we find a…
Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This…
Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…
We examine an application of the kernel-based interpolation to numerical solutions for Zakai equations in nonlinear filtering, and aim to prove its rigorous convergence. To this end, we find the class of kernels and the structure of…
Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate…
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…
Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…
Modern machine learning systems based on neural networks have shown great success in learning complex data patterns while being able to make good predictions on unseen data points. However, the limited interpretability of these systems…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
Interpolation is responsible for digital signal resampling and can significantly degrade the original signal quality if not done properly. For many years, optimal interpolation algorithms were sought within constrained classes of…
In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a $K$-invariant measure $\mu$ with full support, we show that conditional positive…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…
Deep Neural Networks have now achieved state-of-the-art results in a wide range of tasks including image classification, object detection and so on. However, they are both computation consuming and memory intensive, making them difficult to…
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…