Given a finite number of moments of an unknown density on a finite measure space, the best entropy estimate-that nonnegative density x with the given moments which minimizes the Boltzmann-Shannon entropy I(x):= x log x-is considered. A direct proof is given that I has the Kadec property in L-if Yn converges weakly to 37 and I(yn) converges to I(37), then yn converges to 37 in norm. As a corolla...

In this paper, we propose a Robust Discriminant Analysis based on maximum entropy (MaxEnt) criterion (MaxEnt-RDA), which is derived from a nonparametric estimate of Renyi’s quadratic entropy. MaxEnt-RDA uses entropy as both objective and constraints; thus the structural information of classes is preserved while information loss is minimized. It is a natural extension of LDA from Gaussian assump...

We outline four ways in which uncertainty might affect comprehension difficulty in human sentence processing. These four hypotheses motivate a self-paced reading experiment, in which we used verb subcategorization distributions to manipulate the uncertainty over the next step in the syntactic derivation (single step entropy) and the surprisal of the verb’s complement. We additionally estimate w...

We study the convergence to equilibrium of a class of nonlinear recombination models. In analogy with Boltzmann’s H theorem from kinetic theory, and in contrast with previous analysis of these models, convergence is measured in terms of relative entropy. The problem is formulated within a general framework that we refer to as Reversible Quadratic Systems. Our main result is a tight quantitative...

Minimization problems involving @-entropyfunctionals (ageneralization of Boltzmann-Shannon entropy) are studied over a givenset A and a sequence of sets A, and the properties of their optimalsolutions I@,I,. Under certain conditions on the objective functional andthe sets A and A,, it is proven that as n increases to infinity, the optimalsolution I, converges in Llno...

A cross-sectional study evaluated 182 students in the last two years of medical school and 70 residents of a national hospital in Peru on the risk indicators used for reporting results in clinical trials. A questionnaire was used to assess the ability to recognize and calculate risk indicators most widely used in the epidemiological literature. From the participants, 19.4% did not recognize any...