Related papers: Maximum entropy and the problem of moments: A stab…
In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
In this paper we propose a new Eulerian modeling and related accurate and robust numerical methods, describing polydisperse evaporating sprays, based on high order moment methods in size. The main novelty of this model is its capacity to…
We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion…
Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model. We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
Max stable laws are limit laws of linearly normalized partial maxima of indepen- dent, identically distributed (iid) random variables (rvs). These are analogous to stable laws which are limit laws of normalized partial sums of iid rvs. In…
Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
After the justification of the maximum entropy approach for equilibrium thermodynamic system, and of a maximum path entropy algorithm for nonequilibrium thermodynamic systems by virtue of the principle of virtual work, we present in this…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
It is supposed that the exponential multiplier in the method of the non-equilibrium statistical operator (Zubarev`s approach) can be considered as a distribution density of the past lifetime of the system, and can be replaced by an…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…