Related papers: A Mutual Information Approach to Calculating Nonli…
Since its inception, the neural estimation of mutual information (MI) has demonstrated the empirical success of modeling expected dependency between high-dimensional random variables. However, MI is an aggregate statistic and cannot be used…
In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…
In this paper, we propose a novel axiomatic approach to evaluating the joint risk of multiple insurance risks under dependence uncertainty. Motivated by both the theory of expected utility and the Cobb-Dauglas utility function, we establish…
Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been…
A method to estimate the time-dependent correlation via an empirical bias estimate of the time-delayed mutual information for a time-series is proposed. In particular, the bias of the time-delayed mutual information is shown to often be…
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…
Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…
Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined. The measures are expressed as the sum of lagged dependence and instantaneous dependence.…
Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these…
We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for…
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…
Partial information decomposition (PID) of the multivariate mutual information describes the distinct ways in which a set of source variables contains information about a target variable. The groundbreaking work of Williams and Beer has…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
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…