相关论文: Equivalence of distance-based and RKHS-based stati…
Over the last decade, an approach that has gained a lot of popularity to tackle nonparametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of…
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…
Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…
In this article a new family of tests is proposed for the comparison problem of the equality of distribution of two-sample under right censoring scheme. The tests are based on energy distance and kernels mean embedding, are calibrated by…
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…
The distribution closeness testing (DCT) assesses whether the distance between a distribution pair is at least $\epsilon$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete one-dimensional…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…
For statistical inference on an infinite-dimensional Hilbert space $\H $ with no moment conditions we introduce a new class of energy distances on the space of probability measures on $\H$. The proposed distances consist of the integrated…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…
The Maximum Mean Discrepancy (MMD) is a widely used multivariate distance metric for two-sample testing. The standard MMD test statistic has an intractable null distribution typically requiring costly resampling or permutation approaches…
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…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
We reprove the well known fact that the energy distance defines a metric on the space of Borel probability measures on a Hilbert space with finite first moment by a new approach, by analyzing the behavior of the Gaussian kernel on Hilbert…
Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering…
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…
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…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…