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The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly…

Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy…

Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…

In computer vision, it is often observed that formulating regression problems as a classification task often yields better performance. We investigate this curious phenomenon and provide a derivation to show that classification, with the…

The entropy of a closure operator has been recently proposed for the study of network coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank…

The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created…

A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a…

The pervasiveness of proprietary language models has raised critical privacy concerns, necessitating advancements in private inference (PI), where computations are performed directly on encrypted data without revealing users' sensitive…

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

Volcanic regions have shaped human settlements for millennia, placing over 500 million people worldwide within close proximity to active volcanoes. Predicting eruptions that threaten both lives and property remains a critical challenge,…

The metaphor of a potential epigenetic differentiation landscape broadly suggests that during differentiation a stem cell follows the steepest descending gradient toward a stable equilibrium state which represents the final cell type. It…

We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…

The rapid scaling of artificial intelligence models has revealed a fundamental tension between model capacity (storage) and inference efficiency (computation). While classical information theory focuses on transmission and storage limits,…

This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…

Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schuermann, which itself is a generalization of an estimator proposed…

The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets.…

Expert finding is an information retrieval task concerned with the search for the most knowledgeable people, in some topic, with basis on documents describing peoples activities. The task involves taking a user query as input and returning…

This paper presents a command-line tool, called Entropia, that implements a family of conformance checking measures for process mining founded on the notion of entropy from information theory. The measures allow quantifying classical…