Related papers: Optimal Guessing under Nonextensive Framework and …
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the…
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
We consider a new framework where a continuous, though bounded, random variable has unobserved bounds that vary over time. In the context of univariate time series, we look at the bounds as parameters of the distribution of the bounded…
In this paper, we address the problem of bounding conditional expectations when moment information of the underlying distribution and the random event conditioned upon are given. To this end, we propose an adapted version of the generalized…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…
In this paper, we present a technically simple method to establish upper bounds on the expected injective norm of real and complex random tensors. Our approach is somewhat analogous to the moment method in random matrix theory, and is based…
What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium? Here, we…
The definition of probabilities in eternally inflating universes requires a measure to regulate the infinite spacetime volume, and much of the current literature uses a global time cutoff for this purpose. Such measures have been found to…
Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…
The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…
The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and…
In this paper, we investigate new procedures for statistical testing based on Tsallis entropy, a parametric generalization of Shannon entropy. Focusing on multivariate generalized Gaussian and $q$-Gaussian distributions, we develop…
Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…