Related papers: A Note on Optimizing Distributions using Kernel Me…
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
The kernel $k$-means is an effective method for data clustering which extends the commonly-used $k$-means algorithm to work on a similarity matrix over complex data structures. The kernel $k$-means algorithm is however computationally very…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…
The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…
A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability…
Kernel smoothers are considered near the boundary of the interval. Kernels which minimize the expected mean square error are derived. These kernels are equivalent to using a linear weighting function in the local polynomial regression. It…
Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each…
A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given finite samples, an…
In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…
We develop some theoretical results for a robust similarity measure named "generalized min-max" (GMM). This similarity has direct applications in machine learning as a positive definite kernel and can be efficiently computed via…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
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…
Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…