Scientists are assembling sequence data sets from increasing numbers of species and genes to build comprehensive timetrees. However, data are often unavailable for some species and gene combinations, and the proportion of missing data is often large for data sets containing many genes and species. Surprisingly, there has not been a systematic analysis of the effect of the degree of sparseness o...

Scientists are assembling sequence data sets from increasing numbers of species and genes to build comprehensive timetrees. However, data are often unavailable for some species and gene combinations, and the proportion of missing data is often large for data sets containing many genes and species. Surprisingly, there has not been a systematic analysis of the effect of the degree of sparseness o...

We consider nonparametric estimation of L2, Rényi-α and Tsallis-α divergences between continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them into divergence estimators. For the integral functionals, our estimators are based on corrections of a preliminary plug-in estimator. We show that these estimators achieve t...

Abstract Taylor’s polynomial and Green’s function are used to obtain new generalizations of an inequality for higher order convex functions containing Csiszár divergence on time scales. Various inequalities some measures in quantum calculus h -discrete also established.

1 Deviation bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Markov and generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Class of sub-Gaussian random variables . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2....

This paper discusses a local parametric modeling by the use of U-divergence in a statistical pattern recognition. The class of U-divergence measures commonly has an empirical loss function in a simple form including Kullback-Leibler divergence, the power divergence and mean squared error. We propose a minimization algorithm for parametric models of sequentially increasing dimension by incorpora...

Goal: estimation of high dimensional information theoretical quantities (entropy, mutual information, divergence). • Problem: computation/estimation is quite slow. • Consistent estimation is possible by nearest neighbor (NN) methods [1] → pairwise distances of sample points: – expensive in high dimensions [2], – approximate isometric embedding into low dimension is possible (Johnson-Lindenstrau...