Related papers: Total/dual correlation/coherence, redundancy/syner…
We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum…
Based on the Pauli spin operators we develop the notion of the spin-correlation matrix for the two-qubit system. If this matrix is non-zero, the measure of the correlation between the qubits is the average of the non-zero elements.…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
Mutual information in three (or more) dimensions can be considered as a Triple-Helix indicator of synergy in university-industry-government relations. An open-source routine th4.exe makes the computation of this indicator interactively…
Many mathematical modelling tasks (such as in Economics and Finance) are informed by data that is "found" rather than being the result of carefully designed experiments. This often results in data series that are short, noisy,…
When two variables are related by a known function, the coefficient of determination (denoted $R^2$) measures the proportion of the total variance in the observations that is explained by that function. This quantifies the strength of the…
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…
Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the…
Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\Psi({\bf r})$…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
Spuriousness arises when there is an association between two or more variables in a dataset that are not causally related. In this work, we propose an explainability framework to preemptively disentangle the nature of such spurious…
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…
In many scientific tasks we are interested in discovering whether there exist any correlations in our data. This raises many questions, such as how to reliably and interpretably measure correlation between a multivariate set of attributes,…
Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have…
Measurement bridges theory and empirics. Without measures that appropriately capture theoretical concepts, description will fail to represent reality and true causal inference will be impossible. Yet, the social sciences traffic in complex…