Related papers: Conditional Equi-concentration of Types
We extend results on quadratic pressure and convergence of Gibbs mesures from previous joined work of the authors to the Curie-Weiss-Potts model. We define the notion of equilibrium state for the quadratic pressure and show that under some…
We study minimization of a parametric family of relative entropies, termed relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}(P,Q)$). These arise as redundancies under mismatched compression when cumulants of compressed lengths are…
A novel definition of the conditional smooth Renyi entropy, which is different from that of Renner and Wolf, is introduced. It is shown that our definition of the conditional smooth Renyi entropy is appropriate to give lower and upper…
Moment inequalities play important roles in probability limit theory and mathematical statistics. In this work, the von Bahr-Esseen type inequality for extended negatively dependent random variables under sub-linear expectations is…
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
Erdos-Renyi limit laws give the length scale of a time-window over which time-averages in Birkhoff sums have a non-trivial almost-sure limit. We establish Erdos-Renyi type limit laws for Holder observables on dynamical systems modeled by…
The masses of excited heavy mesons are studied with sum rules in the heavy quark effective theory. A set of interpolating currents creating (annihilating) excited heavy mesons with arbitrary spin and parity are proposed and their properties…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…
In this paper, some ?-classes of weighted conditional expectation type operators, such as A-class, ?-A-class and quasi-?-A classes on L2(?) are investigated. Also, the spectrum, point spectrum and spectral radius of these operators are…
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
We introduce a class of spatial stochastic processes in the max-domain of attraction of familiar max-stable processes. The new class is based on Cox processes and comprises models with short range dependence. We show that statistical…
We give an interpretation of the Maximum Entropy (MaxEnt) Principle in game-theoretic terms. Based on this interpretation, we make a formal distinction between different ways of {em applying/} Maximum Entropy distributions. MaxEnt has…
We investigate convergence of the expectation maximization algorithm by representing it as a generalized proximal method. Convergence of iterates and not just in value is investigated under natural hypotheses such as definability of the…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…
We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which…
Two topics in heavy quark expansion are discussed. The heavy quark potential in perturbation theory is reviewed in connection to the problem of the heavy quark mass. The nontrivial reason behind the failure of the "potential subtracted"…