Related papers: Boosting the Power of Kernel Two-Sample Tests

In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why…

We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test…

Modern data analyses frequently encounter settings where samples of variables are contaminated by measurement error. Ignoring measurement noise can substantially degrade statistical inference, while existing correction techniques are often…

In this paper we present two related, kernel-based Distance Metric Learning (DML) methods. Their respective models non-linearly map data from their original space to an output space, and subsequent distance measurements are performed in the…

Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each…

We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy…

Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…

This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…

In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…

Maximum mean discrepancy (MMD) has enjoyed a lot of success in many machine learning and statistical applications, including non-parametric hypothesis testing, because of its ability to handle non-Euclidean data. Recently, it has been…

Data depth has emerged as an invaluable nonparametric measure for the ranking of multivariate samples. The main contribution of depth-based two-sample comparisons is the introduction of the Q statistic (Liu and Singh, 1993), a quality…

We present a novel scheme to boost detection power for kernel maximum mean discrepancy based sequential change-point detection procedures. Our proposed scheme features an optimal sub-sampling of the history data before the detection…

In this paper, we bound the error induced by using a weighted skeletonization of two data sets for computing a two sample test with kernel maximum mean discrepancy. The error is quantified in terms of the speed in which heat diffuses from…

Recently in [1, 2], Ali-Akbar Bromideh introduced the Kullback-Leibler Divergence (KLD) test statistic in discrim- inating between two models. It was found that the Ratio Minimized Kulback-Leibler Divergence (RMKLD) works better than the…

Many large-scale testing procedures learn signal structure from the data to boost power. Direct data reuse can inflate Type-I error ("double dipping"), so a common remedy is masking: withholding some information during learning and using it…

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…

The stochastic block model is a popular tool for detecting community structures in network data. Detecting the difference between two community structures is an important issue for stochastic block models. However, the two-sample test has…

Detecting the emergence of abrupt property changes in time series is a challenging problem. Kernel two-sample test has been studied for this task which makes fewer assumptions on the distributions than traditional parametric approaches.…

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…