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Maximum mean discrepancy (MMD) has been widely adopted in domain adaptation to measure the discrepancy between the source and target domain distributions. Many existing domain adaptation approaches are based on the joint MMD, which is…

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically…

A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…

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…

Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…

This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or…

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…

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…

Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit…

Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc…

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…

As recent literature has demonstrated how classifiers often carry unintended biases toward some subgroups, deploying machine learned models to users demands careful consideration of the social consequences. How should we address this…

In this paper, we propose a general framework to learn a robust large-margin binary classifier when corrupt measurements, called anomalies, caused by sensor failure might be present in the training set. The goal is to minimize the…

Conditional Maximum Mean Discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions, thus it has been successfully used for pattern classification. However, CMMD does…

While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…

Given observations from a positive random variable contaminated by multiplicative measurement error, we consider a nonparametric goodness-of-fit testing task for its unknown density in a non-asymptotic framework. We propose a testing…

Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain…

Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…

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…