相关论文: Mutual Dependence: A Novel Method for Computing De…
Mutual information is an important measure of the dependence among variables. It has become widely used in statistics, machine learning, biology, etc. However, the standard techniques for estimating it often perform poorly in higher…
Recently established, directed dependence measures for pairs $(X,Y)$ of random variables build upon the natural idea of comparing the conditional distributions of $Y$ given $X=x$ with the marginal distribution of $Y$. They assign pairs…
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of…
Quantifying cooperation or synergy among random variables in predicting a single target random variable is an important problem in many complex systems. We review three prior information-theoretic measures of synergy and introduce a novel…
We introduce Network Maximal Correlation (NMC) as a multivariate measure of nonlinear association among random variables. NMC is defined via an optimization that infers transformations of variables by maximizing aggregate inner products…
We consider the distributed detection problem of a temporally correlated random radio source signal using a wireless sensor network capable of measuring the energy of the received signals. It is well-known that optimal tests in the…
We propose the exact calculation of the probability density function (PDF) and cumulative distribution function (CDF) of mutual information (MI) for a two-user MIMO MAC network over block Rayleigh fading channels. So far the PDF and CDF…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
This paper develops new methodology, together with related theories, for combining information from independent studies through confidence distributions. A formal definition of a confidence distribution and its asymptotic counterpart (i.e.,…
Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…
We propose a novel estimator of the mutual information between two ordinal vectors $x$ and $y$. Our approach is inductive (as opposed to deductive) in that it depends on the data generating distribution solely through some nonparametric…
Pearson's correlation is an important summary measure of the amount of dependence between two variables. It is natural to want to generalise the concept of correlation as a single number that measures the inter-relatedness of three or more…
Mutual Information (MI) is a crucial measure for capturing dependencies between variables, but exact computation is challenging in high dimensions with intractable likelihoods, impacting accuracy and robustness. One idea is to use an…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
In this paper, distributed Bayesian detection problems with unknown prior probabilities of hypotheses are considered. The sensors obtain observations which are conditionally dependent across sensors and their probability density functions…
The identification of relevant features, i.e., the driving variables that determine a process or the properties of a system, is an essential part of the analysis of data sets with a large number of variables. A mathematical rigorous…