Related papers: Neurally-plausible radial basis kernels using dist…
Kernel-based methods are heavily used in machine learning. However, they suffer from $O(N^2)$ complexity in the number $N$ of considered data points. In this paper, we propose an approximation procedure, which reduces this complexity to…
Implicit Neural Representations (INR) use multilayer perceptrons to represent high-frequency functions in low-dimensional problem domains. Recently these representations achieved state-of-the-art results on tasks related to complex 3D…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…
The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…
Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…
Characterizing the function spaces defined by neural networks helps understanding the corresponding learning models and their inductive bias. While in some limits neural networks correspond to function spaces that are Hilbert spaces, these…
The normalized radial basis function neural network emerges in the statistical modeling of natural laws that relate components of multivariate data. The modeling is based on the kernel estimator of the joint probability density function…
In this article, we consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, Newton, Poisson kernels and spherical functions, i.e. the…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
We study the mixtures of factorizing probability distributions represented as visible marginal distributions in stochastic layered networks. We take the perspective of kernel transitions of distributions, which gives a unified picture of…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a…
Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate…
The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…