Related papers: Measuring Statistical Dependencies via Maximum Nor…
This short note suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak and such that the traditional methods are not effective. The method requires…
This article proposes a novel test for the martingale difference hypothesis based on the martingale difference divergence function, a recently developed dependence measure suitable for measuring the degree of conditional mean dependence of…
Reliable measurement of dependence between variables is essential in many applications of statistics and machine learning. Current approaches for dependence estimation, especially density-based approaches, lack in precision, robustness…
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…
We introduce a framework for filtering features that employs the Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence between the features and the labels. The key idea is that good features should maximise such…
To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…
This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…
The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…
Modern longitudinal data, for example from wearable devices, measures biological signals on a fixed set of participants at a diverging number of time points. Traditional statistical methods are not equipped to handle the computational…
This paper focuses on a data-rich environment where the data set has a very large cross-sectional dimension, is likely to exhibit local dependence, and yet is hard to determine the dependence ordering. Such a situation arises, for example,…
We present a novel framework for learning system design with neural feature extractors. First, we introduce the feature geometry, which unifies statistical dependence and feature representations in a function space equipped with inner…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…
We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the…
In this paper, we use a probabilistic model to estimate the number of uncorrelated features in a large dataset. Our model allows for both pairwise feature correlation (collinearity) and interdependency of multiple features…
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
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…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
We generalize 2-Wasserstein dependence coefficients to measure dependence between a finite number of random vectors. This generalization includes theoretical properties, and in particular focuses on an interpretation of maximal dependence…
Heuristic-based methods are among the most popular methods in the process discovery area. This category of methods is composed of two main steps: 1) discovering a dependency graph 2) determining the split/join patterns of the dependency…