Related papers: Bounding the Error From Reference Set Kernel Maxim…
This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…
We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…
Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…
This paper presents novel generalization bounds for the multi-kernel learning problem. Motivated by applications in sensor networks and spatial-temporal models, we assume that the dataset is mixed where each sample is taken from a finite…
The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…
Non-parametric two-sample tests based on energy distance or maximum mean discrepancy are widely used statistical tests for comparing multivariate data from two populations. While these tests enjoy desirable statistical properties, their…
We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…
Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…
Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…
To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly…
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…
Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error…
We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…
Mixed-precision computing has become increasingly important in modern high-performance computing and machine learning applications. When implementing custom mixed-precision functions -- such as fused operators, optimized GPU kernels, or…
We develop two approaches for analyzing the approximation error bound for the Nystr\"{o}m method, one based on the concentration inequality of integral operator, and one based on the compressive sensing theory. We show that the…
The relative similarity testing aims to determine which of the distributions, P or Q, is closer to an anchor distribution U. Existing kernel-based approaches often test the relative similarity with a fixed kernel in a manually specified…
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…
In this PhD thesis, we propose a novel framework for uncertainty quantification in machine learning, which is based on proper scores. Uncertainty quantification is an important cornerstone for trustworthy and reliable machine learning…