Related papers: Maximum Entropy approach to a Mean Field Theory fo…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
The Maximum Entropy Modeling Toolkit supports parameter estimation and prediction for statistical language models in the maximum entropy framework. The maximum entropy framework provides a constructive method for obtaining the unique…
We consider a static self-gravitating system consisting of perfect fluid with isometries of an $(n-2)$-dimensional maximally symmetric space in Lovelock gravity theory. A straightforward analysis of the time-time component of the equations…
I employ the van der Waals theory of Baus and coworkers to analyze the fast, adiabatic decay of a supercooled liquid in a closed vessel with which the solidification process usually starts. By imposing a further constraint on either the…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…
This note presents Godunov variables and 4-potentials for the relativistic Euler equations of barotropic fluids. The associated additional conservation/ production law has different interpretations for different fluids. In particular it…
The principle of maximum entropy is applied to the spectral analysis of a data signal with general variance matrix and containing gaps in the record. The role of the entropic regularizer is to prevent one from overestimating structure in…
By developing a new technique called the bi-coupling argument, we estimate the relative entropy between different diffusion processes in terms of the distances of initial distributions and drift-diffusion coefficients. As an application,…
Based on the variational field theory framework, we extend our previous mean-field formalism, taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that…
During the MaxEnt 2002 workshop in Moscow, Idaho, Tony Vignaux asked again a few simple questions about using Maximum Entropy or Bayesian approaches for the famous Dice problems which have been analyzed many times through this workshop and…
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…
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…
Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…
Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…
It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here, we…
We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction…
We introduce a definition of coarse-grained entropy that unifies measurement-based (observational entropy) and max-entropy-based (Jaynes) approaches to coarse-graining, by identifying physical constraints with information theoretic priors.…
Given a knowledge base KB containing first-order and statistical facts, we consider a principled method, called the random-worlds method, for computing a degree of belief that some formula Phi holds given KB. If we are reasoning about a…
Dynamics of many-particle systems with long-range interaction is collisionless and governed by the Vlasov equation. This dynamics is a flow of a six-dimensional incompressible liquid with uncountable integrals of motion. If the flow…