相关论文: The Entropy Method in Large Deviation Theory
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
Boltzmann-Sanov and Cramer-Chernoff's theorems provide large deviation probabilities, entropy, and rate functions for the spatial distribution of systems and the total internal energy of an ensemble respectively. By the method of Lagrange's…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
This work is devoted to a vast extension of Sanov's theorem, in Laplace principle form, based on alternatives to the classical convex dual pair of relative entropy and cumulant generating functional. The abstract results give rise to a…
Large deviation theory is a branch of probability theory that is devoted to a study of the "rate" at which empirical estimates of various quantities converge to their true values. The object of study in this paper is the rate at which…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x_1^n using the entropy of the k-block empirical probability and letting k grow with $n$ roughly like log n. We further assume that the…
We demonstrate that the shallow water moment equations satisfy an auxiliary entropy conservation law, where the entropy function corresponds to the total energy. Additionally, we show that the classical Newtonian slip friction and Manning…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the…
We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some…
We apply the G\"artner--Ellis theorem on large deviations to prove a weak version of the Loughran--Smeets conjecture for general fibrations.
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
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…
We consider the problem of approximating the von Neumann entropy of a large, sparse, symmetric positive semidefinite matrix $A$, defined as $\operatorname{tr}(f(A))$ where $f(x)=-x\log x$. After establishing some useful properties of this…
We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…