Related papers: On Asymptotic Properties of Hyperparameter Estimat…

There has been a resurgence of interest in incomplete U-statistics that only sum over a subset of kernel evaluations, due to their computational efficiency and asymptotic normality which can be leveraged to quantify the uncertainty of…

Kernel-based feature selection is an important tool in nonparametric statistics. Despite many practical applications of kernel-based feature selection, there is little statistical theory available to support the method. A core challenge is…

This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…

The rate of convergence of weighted kernel herding (WKH) and sequential Bayesian quadrature (SBQ), two kernel-based sampling algorithms for estimating integrals with respect to some target probability measure, is investigated. Under…

We consider nonparametric inference of finite dimensional, potentially non-pathwise differentiable target parameters. In a nonparametric model, some examples of such parameters that are always non pathwise differentiable target parameters…

Batch Bayesian optimisation and Bayesian quadrature have been shown to be sample-efficient methods of performing optimisation and quadrature where expensive-to-evaluate objective functions can be queried in parallel. However, current…

Methods for medical image registration infer geometric transformations that align pairs/groups of images by maximising an image similarity metric. This problem is ill-posed as several solutions may have equivalent likelihoods, also…

We study the high-dimensional asymptotics of empirical risk minimization (ERM) in over-parametrized two-layer neural networks with quadratic activations trained on synthetic data. We derive sharp asymptotics for both training and test…

Modern approaches for simulation-based inference rely upon deep learning surrogates to enable approximate inference with computer simulators. In practice, the estimated posteriors' computational faithfulness is, however, rarely guaranteed.…

The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…

Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…

We develop an empirical Bayes (EB) G-modeling framework for short-panel linear models with nonparametric prior for the random intercepts, slopes, dynamics, and non-spherical error variances. We establish identification and consistency of…

Automatic speech recognition (ASR) outcomes serve as input for downstream tasks, substantially impacting the satisfaction level of end-users. Hence, the diagnosis and enhancement of the vulnerabilities present in the ASR model bear…

We unify $\textit{kernel density estimation}$ and $\textit{empirical Bayes}$ and address a set of problems in unsupervised learning with a geometric interpretation of those methods, rooted in the $\textit{concentration of measure}$…

Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…

The Helstrom measurement (HM) is known to be the optimal strategy for distinguishing non-orthogonal quantum states with minimum error. Previously, a binary classifier based on classical simulation of the HM has been proposed. It was…

We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum…

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model…