Related papers: Multivariate Differential Association Analysis
Multivariate correlation analysis plays a key role in various fields such as statistics and big data analytics. In this paper, it is presented a new non-parametric association measure between more than two variables based on the concept of…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting non-linear, non-monotone relationships,…
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…
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…
It is frequently of interest to jointly analyze two paired sequences of multiple tests. This paper studies the problem of detecting whether there are more pairs of tests that are significant in both sequences than would be expected by…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
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…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…
Unsupervised two-view learning, or detection of dependencies between two paired data sets, is typically done by some variant of canonical correlation analysis (CCA). CCA searches for a linear projection for each view, such that the…
Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…
Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high-dimensionality of networks pose unique challenges to traditional dependency…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…
A fundamental task in AI is to assess (in)dependence between mixed-type variables (text, image, sound). We propose a Bayesian kernelised correlation test of (in)dependence using a Dirichlet process model. The new measure of (in)dependence…
In the presence of weak overall correlation, it may be useful to investigate if the correlation is significantly and substantially more pronounced over a subpopulation. Two different testing procedures are compared. Both are based on the…
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…