A Characterization of Entropies of Degree a.
A free analogue of the transportation cost inequality on the circle
A general class of entropy statistics
To study the asymptotic properties of entropy estimates, we use a unified expression, called the -entropy. Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators are considered, so they can be used to construct confidence intervals and to test statistical hypotheses based on one or more samples. These results can also be applied to multinomial populations.
A generalization of Bellman's functional equation.
A generalization of entropy equation: homogeneous entropies
A generalized Fannes' inequality.
A generalized residual information measure and its properties.
A geometry on the space of probabilities (I). The finite dimensional case.
In this note we provide a natural way of defining exponential coordinates on the class of probabilities on the set Ω = [1,n] or on P = {p = (p1, ..., pn) ∈ Rn| pi > 0; Σi=1n pi = 1}. For that we have to regard P as a projective space and the exponential coordinates will be related to geodesic flows in Cn.
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A log-Sobolev type inequality for free entropy of two projections
We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.
A measure of mutual divergence among a number of probability distributions.
A mixed theory of information. I : symmetric, recursive and measurable entropies of randomized systems of events
A mixed theory of information - VIII: Inset measures depending upon several distributions.
A mixed theory of information - VIII: Inset measures depending upon several distributions. (Short Communication).
A Mixid Theory of Information - IV: Inset-Inaccuracy and Directed Divergence.
A new approach to mutual information
A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
A new approach to mutual information. II
A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.
A new generalization of entropy and its characterization
A note on the interval-valued marginal problem and its maximum entropy solution
This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.
A representation theorem for entropies with the branching property.