We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is applied to the measurements. A link function can also be used to define an alternative structure on a set. We will see that generalized entropies are equivalen...

This work investigates three aspects: (a) a network vulnerability as the non-uniform vulnerable-host distribution, (b) threats, i.e., intelligent malwares that exploit such a vulnerability, and (c) defense, i.e., challenges for fighting the threats. We first study five large data sets and observe consistent clustered vulnerable-host distributions. We then present a new metric, referred to as th...

Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for Rényi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we s...

Maximum Entropy (MaxEnt) models (Jaynes, 1957) are exponential models that implement the intuition that if there is no evidence to favour one alternative solution above another, both alternatives should be equally likely. In order to accomplish this, as much information as possible about the process you want to model must be collected. This information consists of frequencies of events relevant...

The main statistics used in rough set data analysis, the approximation quality, is of limited value when there is a choice of competing models for predicting a decision variable. In keeping within the rough set philosophy of non–invasive data analysis, we present three model selection criteria, using information theoretic entropy in the spirit of the minimum description length principle. Our ma...

I present empirical comparisons between a standard statistical translation model and an equivalent Maximum Entropy model. Results show that the Maximum Entropy model is promising, but highly sensitive to the method of feature selection.

We study conditional computational entropy: the amount of randomness a distribution appears to have to a computationally bounded observer who is given some correlated information. By considering conditional versions of HILL entropy (based on indistinguishability from truly random distributions) and Yao entropy (based on incompressibility), we obtain: – a separation between conditional HILL and ...

Abstract In this paper, we propose a new spatial interaction model for trip-chaining behavior that consists of a sequence of movements. Particularly, including the origin-destination constraints, we generalize the traditional entropy maximizing model to deal with trip-chaining behaviors. Traditional entropy models should be noted in terms of a theoretical derivation of the gravity model and its...

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex measures of risk, which for a given probabilistic model entails evaluating a financial position by cons...

It is shown that distributions arising in Rényi-Tsallis maximum entropy setting are related to the Generalized Pareto Distributions (GPD) that are widely used for modeling the tails of distributions. The relevance of such modelization, as well as the ubiquity of GPD in practical situations follows from Balkema-De Haan-Pickands theorem on the distribution of excesses (over a high threshold). We ...