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In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
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…
In probability theory, the independence is a very fundamental concept, but with a little mystery. People can always easily manipulate it logistically but not geometrically, especially when it comes to the independence relationships among…
We propose a framework combining detrended fluctuation analysis with standard regression methodology. The method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and…
A range of charts with different strengths and weaknesses exists to support the visual analysis of univariate distributions, with a limited understanding of which charts best support which tasks and users, and how practitioners use charts.…
Distance covariance is a widely used statistical methodology for testing the dependency between two groups of variables. Despite the appealing properties of consistency and superior testing power, the testing results of distance covariance…
A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are…
The evaluation of mathematical results plays a central role in assessing researchers' contributions and shaping the direction of the field. Currently, such evaluations rely primarily on human judgment, whether through journal peer review or…
The global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are the natural methods to study the brain.…
This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate…
The notion of a zenpath and a zenplot is introduced to search and detect dependence in high-dimensional data for model building and statistical inference. By using any measure of dependence between two random variables (such as correlation,…
The advent of high-throughput sequencing technologies has lead to vast comparative genome sequences. The construction of gene-gene interaction networks or dependence graphs on the genome scale is vital for understanding the regulation of…
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
A rank-invariant clustering of variables is introduced that is based on the predictive strength between groups of variables, i.e., two groups are assigned a high similarity if the variables in the first group contain high predictive…
Symbolic Data Analysis works with variables for which each unit or class of units takes a finite set of values/categories, an interval or a distribution (an histogram, for instance). When to each observation corresponds an empirical…
It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or…