Related papers: Universalities of Reproducing Kernels Revisited
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…
Dot product kernels, such as polynomial and exponential (softmax) kernels, are among the most widely used kernels in machine learning, as they enable modeling the interactions between input features, which is crucial in applications like…
The standard definition of pedestrian density produces scattered values, hence, many approaches have been developed to improve the features of the estimated density. This paper provides a review of generally applied methods and presents a…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…
Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
In this paper we study modified kernel polynomials: $u_n(x) = \sum_{k=0}^n c_k g_k(x)$, depending on parameters $c_k>0$, where $\{ g_k \}_0^\infty$ are orthonormal polynomials on the real line. Besides kernel polynomials with $c_k =…
Bursts of images exhibit significant self-similarity across both time and space. This motivates a representation of the kernels as linear combinations of a small set of basis elements. To this end, we introduce a novel basis prediction…
Kernel ridge regression is well-known to achieve minimax optimal rates in low-dimensional settings. However, its behavior in high dimensions is much less understood. Recent work establishes consistency for kernel regression under certain…
Kernel methods are popular in clustering due to their generality and discriminating power. However, we show that many kernel clustering criteria have density biases theoretically explaining some practically significant artifacts empirically…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
Universality of neural networks describes the ability to approximate arbitrary function, and is a key ingredient to keep the method effective. The established models for universal quantum neural networks(QNN), however, require the…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
Recent applications of kernel methods in machine learning have seen a renewed interest in the Laplacian kernel, due to its stability to the bandwidth hyperparameter in comparison to the Gaussian kernel, as well as its expressivity being…
We study both canonical reproducing kernels and constructive reproducing kernels for holomorphic functions in $\CC^1$ and $\CC^n$. We compare and contrast the two, and also develop important relations between the two types of kernels. We…
This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalization in learning problems. We establish a direct connection between generalization performance in…
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…
This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…