Related papers: On Conditional Correlations
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
This paper examines a commonly used measure of persuasion whose precise interpretation has been obscure in the literature. By using the potential outcome framework, we define the causal persuasion rate by a proper conditional probability of…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
In literature, different common informations were defined by G\'acs and K\"orner, by Wyner, and by Kumar, Li, and Gamal, respectively. In this paper, we define two generalized versions of common informations, named approximate and exact…
In the present paper, we discuss the Pearson, Spearman, Kendall correlation coefficients and their statistical analogues. We propose a new correlation coefficient r and its statistical analogue. The coefficient r is based on Kendal's and…
This paper proposes a class of estimators for population correlation coefficient when information about the population mean and population variance of one of the variables is not available but information about these parameters of another…
In this work, we analyse how to define a conditional version of Sibson's $\alpha$-Mutual Information. Several such definitions can be advanced and they all lead to different information measures with different (but similar) operational…
Parallel recordings of neural spike counts have revealed the existence of context-dependent noise correlations in neural populations. Theories of population coding have also shown that such correlations can impact the information encoded by…
Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…
This article examines the limitations of Pearson's correlation in selecting predictor variables for linear models. Using mtcars and iris datasets from R, this paper demonstrates the limitation of this correlation measure when selecting a…
Fields like public health, public policy, and social science often want to quantify the degree of dependence between variables whose relationships take on unknown functional forms. Typically, in fact, researchers in these fields are…
Entries of datasets are often collected only if an event occurred: taking a survey, enrolling in an experiment and so forth. However, such partial samples bias classical correlation estimators. Here we show how to correct for such sampling…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
We introduce a flexible parametric mixed effects model for correlated binary data, with parameters that can be directly interpreted as marginal odds ratios. This leads to a robust estimation equation with an optimal weighting matrix being…
Selective rationalization improves neural network interpretability by identifying a small subset of input features -- the rationale -- that best explains or supports the prediction. A typical rationalization criterion, i.e. maximum mutual…
We discuss the notions of mutual information and conditional information for noncomposite systems, classical and quantum; both the mutual information and the conditional information are associated with the presence of hidden correlations in…
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with…
The paper outlines a new development in the Contextuality-by-Default theory as applied to finite systems of binary random variables. The logic and principles of the original theory remain unchanged, but the definition of contextuality of a…