Optimal discrete entropy.
Optimal quantization for the one–dimensional uniform distribution with Rényi--entropy constraints
We establish the optimal quantization problem for probabilities under constrained Rényi--entropy of the quantizers. We determine the optimal quantizers and the optimal quantization error of one-dimensional uniform distributions including the known special cases (restricted codebook size) and (restricted Shannon entropy).
Optimality conditions for maximizers of the information divergence from an exponential family
The information divergence of a probability measure from an exponential family over a finite set is defined as infimum of the divergences of from subject to . All directional derivatives of the divergence from are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for to be a maximizer of the divergence from are presented, including new ones when is not projectable to .
Optimally approximating exponential families
This article studies exponential families on finite sets such that the information divergence of an arbitrary probability distribution from is bounded by some constant . A particular class of low-dimensional exponential families that have low values of can be obtained from partitions of the state space. The main results concern optimality properties of these partition exponential families. The case where is studied in detail. This case is special, because if , then contains all probability...
Ordre et informations sur les expériences non disjointes
Predictability problems of global change as seen through natural systems complexity description. II: Approach.
Predictability problems of global change as seen through natural systems complexity description. I: General statements.
Prediction for Two Processes and the Nehari Problem.
Princip maxima entropie
Properties of unique information
We study the unique information function defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of . We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of , and . Our results are based on a reformulation of the first order conditions...
Pruning and measures of uncertainty
Pseudo-generalization of Shannon inequality for Mittal's entropy and its application in coding theory
Quantification method of classification processes. Concept of structural -entropy
Recent results on the stability of the parametric fundamental equation of information.
Recursive inset entropies of multiplicative type on open domains.
Refinement of the Jensen integral inequality
In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.
Relative entropy and stability of stochastic semigroups
Robust quasi-linear system identification
Several results on set-valued possibilistic distributions
When proposing and processing uncertainty decision-making algorithms of various kinds and purposes, we more and more often meet probability distributions ascribing non-numerical uncertainty degrees to random events. The reason is that we have to process systems of uncertainties for which the classical conditions like -additivity or linear ordering of values are too restrictive to define sufficiently closely the nature of uncertainty we would like to specify and process. In cases of non-numerical...
Shannon entropy: axiomatic characterization and application.