Related papers: On some entropy functionals derived from R\'enyi i…
The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate…
We use a R\'enyi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum or classical communication between two parties. These include state redistribution,…
A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $\rho$-th moment of the number of performed…
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…
In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several…
R\'enyi entropy of order \alpha is a general measure of entropy. In this paper we derive estimations for the R\'enyi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the…
We first observe that the (co)domains of the q-deformed functions are some subsets of the (co)domains of their ordinary counterparts, thereby deeming the deformed functions to be incomplete. In order to obtain a complete definition of…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
Turbulence may appear as a complex process with a multitude of scales and flow patterns, but still obeys simple physical principles such as the conservation of momentum, of energy, and the maximum entropy principle. The latter states that…
We address the question and related controversy of the formulation of the $q$-entropy, and its relative entropy counterpart, for models described by continuous (non-discrete) sets of variables. We notice that an $L_p$ normalized functional…
In this paper, we prove that the Renyi entropy of linearly normalized partial maxima of independent and identically distributed random variables is convergent to the corresponding limit Renyi entropy when the linearly normalized partial…
This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…
The asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the…
Max stable laws are limit laws of linearly normalized partial maxima of indepen- dent, identically distributed (iid) random variables (rvs). These are analogous to stable laws which are limit laws of normalized partial sums of iid rvs. In…
The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they…
We show that the R\'enyi entropies of single particle, extended wave functions for disordered systems contain information about the multifractal spectrum. It is shown for moments of the R\'enyi entropy, $S_{n}$, where $|n|<1$, it is…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy.…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…