Related papers: Permutation-Free High-Order Interaction Tests
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…
Debiased collaborative filtering aims to learn an unbiased prediction model by removing different biases in observational datasets. To solve this problem, one of the simple and effective methods is based on the propensity score, which…
We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
Machine learning and deep learning have been used extensively to classify physical surfaces through images and time-series contact data. However, these methods rely on human expertise and entail the time-consuming processes of data and…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…
Deep artificial neural networks show high predictive performance in many fields, but they do not afford statistical inferences and their black-box operations are too complicated for humans to comprehend. Because positing that a relationship…
In this paper, a class of high order numerical schemes is proposed for solving Hamilton-Jacobi (H-J) equations. This work is regarded as an extension of our previous work for nonlinear degenerate parabolic equations, see Christlieb et al.…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the…
We develop scalable randomized kernel methods for jointly associating data from multiple sources and simultaneously predicting an outcome or classifying a unit into one of two or more classes. The proposed methods model nonlinear…
Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step,…
Kernel regression is an essential and ubiquitous tool for non-parametric data analysis, particularly popular among time series and spatial data. However, the central operation which is performed many times, evaluating a kernel on the data…
Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only…
We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…