Related papers: Efficient Aggregated Kernel Tests using Incomplete…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…
Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative.…
Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require…
We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null…
In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…
Kernel methods provide a flexible and powerful framework for nonparametric statistical testing by embedding probability distributions into a reproducing kernel Hilbert space (RKHS). In this work, we study the kernel two-sample testing…
We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize…
We propose a kernel-based nonparametric test of relative goodness of fit, where the goal is to compare two models, both of which may have unobserved latent variables, such that the marginal distribution of the observed variables is…
Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the…
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…
The maximum mean discrepancy (MMD) is a kernel-based nonparametric statistic for two-sample testing, whose inferential accuracy depends critically on variance characterization. Existing work provides various finite-sample estimators of the…
We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test…
Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…
Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the…
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…
We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the…
We develop a Hilbert--Schmidt independence criterion (HSIC)-based framework for testing serial independence in strictly stationary time series. The proposed auto Hilbert--Schmidt independence criterion (AutoHSIC) measures dependence between…
We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of…
Two-sample tests have been extensively employed in various scientific fields and machine learning such as evaluation on the effectiveness of drugs and A/B testing on different marketing strategies to discriminate whether two sets of samples…
We present a comprehensive study of the commute time kernel method via the effective resistance framework analyzing the quantum complexity of the originally classical approach. Our study reveals that while there is a trade-off between…