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Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…

There is an intense and partly recent literature focussing on the problem of selecting the bandwidth parameter for kernel density estimators. Available methods are largely `very nonparametric', in the sense of not requiring any knowledge…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…

The kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches…

Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…

Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to…

Differential Privacy (DP) is a well-established framework to quantify privacy loss incurred by any algorithm. Traditional formulations impose a uniform privacy requirement for all users, which is often inconsistent with real-world scenarios…

Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…

Comparing conditional distributions is a fundamental challenge in statistics and machine learning, with applications across a wide range of domains. While proposed methods for measuring discrepancies using kernel embeddings of distributions…

Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

Kernel methods play a critical role in many machine learning algorithms. They are useful in manifold learning, classification, clustering and other data analysis tasks. Setting the kernel's scale parameter, also referred to as the kernel's…

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

This paper presents a kernelized version of the t-SNE algorithm, capable of mapping high-dimensional data to a low-dimensional space while preserving the pairwise distances between the data points in a non-Euclidean metric. This can be…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…

We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing…

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…