Related papers: Extending Kernel Testing To General Designs
We study the comparison problem of distribution equality between two random samples under a right censoring scheme. To address this problem, we design a series of tests based on energy distance and kernel mean embeddings. We calibrate our…
Change-point analysis plays a significant role in various fields to reveal discrepancies in distribution in a sequence of observations. While a number of algorithms have been proposed for high-dimensional data, kernel-based methods have not…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
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…
The kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. In this paper we propose a method to boost the power…
To generalize inferences from a randomized trial to the target population of all trial-eligible individuals, investigators can use nested trial designs, where the randomized individuals are nested within a cohort of trial-eligible…
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…
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…
A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational…
This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…
Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing works focused on studying kernel choices to…
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…
We set up a formal framework to characterize encompassing of nonparametric models through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for…
In this paper, we present the general theory of embedding independence tests on Hilbert spaces that generalizes the concepts of distance covariance, distance multivariance and HSIC. This is done by defining new types of kernel on an $n$…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While…