相关论文: Equivalence of distance-based and RKHS-based stati…

We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…

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…

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…

This paper adresses the problem of testing for the equality of $k$ probability distributions on Hilbert spaces, with $k\geqslant 2$. We introduce a generalization of the maximum variance discrepancy called multiple maximum variance…

The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…

We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac…

Metric learning from a set of triplet comparisons in the form of "Do you think item h is more similar to item i or item j?", indicating similarity and differences between items, plays a key role in various applications including image…

Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…

Weighted log-rank tests are arguably the most widely used tests by practitioners for the two-sample problem in the context of right-censored data. Many approaches have been considered to make weighted log-rank tests more robust against a…

Much recent work in bioinformatics has focused on the inference of various types of biological networks, representing gene regulation, metabolic processes, protein-protein interactions, etc. A common setting involves inferring network edges…

Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert…

The recent developments in machine learning have highlighted a conflict between online platforms and their users in terms of privacy. The importance of user privacy and the struggle for power over user data has been intensified as…

This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally…

Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive…

Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…

This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…

M-estimators offer simple robust alternatives to the maximum likelihood estimator. Much of the robustness literature, however, has focused on the problems of location, location-scale and regression estimation rather than on estimation of…