相关论文: Comparing distributions: $\ell_1$ geometry improve…

Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…

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 adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly…

In this paper we compare two regression curves by measuring their difference by the area between the two curves, represented by their $L^1$-distance. We develop asymptotic confidence intervals for this measure and statistical tests to…

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…

Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…

We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

Nonparametric detection of existence of an anomalous structure over a network is investigated. Nodes corresponding to the anomalous structure (if one exists) receive samples generated by a distribution q, which is different from a…

We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…

In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low sample size setting. Our test statistics include the well-known energy distance and maximum mean discrepancy with…

Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification. In this paper, we develop a method for comparing how close different generative…

In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…

Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…

The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot…

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean…

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…

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…

We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…