Related papers: Maximum entropy copula with given diagonal section
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
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…
The routine definitions of both entropy, and differential entropy show inconsistencies that make them not reciprocally coherent. We propose a few possible modifications of these quantities so that 1) they no longer show incongruities, 2)…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
In spite of the Lebesgue density theorem, there is a positive $\delta$ such that, for every non-trivial measurable set $S$ of real numbers, there is a point at which both the lower densities of $S$ and of the complement of $S$ are at least…
Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally suitable, possibilities. Following Jaynes'…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
In this note we construct measures of maximal entropy for a certain class of maps with critical points called Viana maps. The main ingredients of the proof are the non-uniform expansion features and the slow recurrence (to the critical set)…
The number of allowed configurations of a polymer is reduced by the presence of a repulsive surface resulting in an entropic force between them. We develop a method to calculate the entropic force, and detailed pressure distribution, for…
Motivated by modern applications like image processing and wireless sensor networks, we consider a variation of the famous Kepler Conjecture. Given any infinite set of unit balls covering the whole space, we want to know the optimal (lim…
The classical tail dependence coefficient (TDC) may fail to capture non-exchangeable features of bivariate tail dependence since it evaluates the underlying copula only along the diagonal. To address this limitation, several measures of…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
Recent findings for optimal transport maps between distribution functions sharing the same copula show that componentwise the solution is the optimal map between marginal distributions. This is an important discovery since in the…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
Given a collection of probability distributions $p_{1},\ldots,p_{m}$, the minimum entropy coupling is the coupling $X_{1},\ldots,X_{m}$ ($X_{i}\sim p_{i}$) with the smallest entropy $H(X_{1},\ldots,X_{m})$. While this problem is known to be…
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…
The maximum entropy of a quantized surface is demonstrated to be proportional to the surface area in the classical limit. The result is valid in loop quantum gravity, and in a somewhat more general class of approaches to surface…
This is a review and tutorial paper which discusses the fundamental limitations on the maximal power which can be received, absorbed, and scattered by an electrically small electrically polarizable particle and infinite periodical arrays of…