Related papers: A Kernel Stein Test for Comparing Latent Variable …

We consider the goodness of fit testing problem for linear stochastic differential equation (Ornstein-Uhlenbeck process). The basic hypothesis is supposed to be composite with two-dimensional unknown parameter. We study two goodness of fit…

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…

The Maximum Mean Discrepancy (MMD) has been the state-of-the-art nonparametric test for tackling the two-sample problem. Its statistic is given by the difference in expectations of the witness function, a real-valued function defined as a…

Existing example-based prediction explanation methods often bridge test and training data points through the model's parameters or latent representations. While these methods offer clues to the causes of model predictions, they often…

In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…

Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and…

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the…

Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires…

We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central…

The nonparametric problem of detecting existence of an anomalous interval over a one dimensional line network is studied. Nodes corresponding to an anomalous interval (if exists) receive samples generated by a distribution q, which is…

Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…

Linear stochastic transitivity is a central assumption in paired comparison models that is rarely verified in practice. Empirical violations, however, are common and can substantially affect inference and ranking. We develop a class of…

We propose kernel-type smoothed Kolmogorov-Smirnov and Cram\'{e}r-von Mises tests for data on general interval, using bijective transformations. Though not as severe as in the kernel density estimation, utilizing naive kernel method…

We propose a novel supervised learning method to optimize the kernel in the maximum mean discrepancy generative adversarial networks (MMD GANs), and the kernel support vector machines (SVMs). Specifically, we characterize a distributionally…

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

Stein discrepancies have emerged as a powerful statistical tool, being applied to fundamental statistical problems including parameter inference, goodness-of-fit testing, and sampling. The canonical Stein discrepancies require the…

Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to…

Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…

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…

In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous…