Related papers: Minimum relative entropy distributions with a larg…
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…
In this short note we study the asymptotic behaviour of the minima over compact intervals of Gaussian processes, whose paths are not necessarily smooth. We show that, beyond the logarithmic large deviation Gaussian estimates, this problem…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
We consider a Bayesian problem of estimating of probability of success in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of differential entropy for posterior probability density…
According to a general probabilistic principle, the natural divisors of friable integers (i.e.~free of large prime factors) should normally present a Gaussian distribution. We show that this indeed is the case with conditional density…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of…
Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random…
It is argued that a Gibbsian formula for the space-time distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy…
A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving…
Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…
In this note, we show that the relative entropy of an empirical distribution of $n$ samples drawn from a set of size $k$ with respect to the true underlying distribution is exponentially concentrated around its expectation, with central…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
Minimization of the (regularized) entropy of classification probabilities is a versatile class of discriminative clustering methods. The classification probabilities are usually defined through the use of some classical losses from…
The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize…
We consider the problem of determining the top-$k$ largest measurements from a dataset distributed among a network of $n$ agents with noisy communication links. We show that this scenario can be cast as a distributed convex optimization…
Let X_n=(x_{ij}) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let R_n=(\rho_{ij}) be the p\times p sample correlation matrix of X_n; that is, the entry…