Related papers: Impossible Mission: Entropy Maximization with Esco…
Current unsupervised anomaly localization approaches rely on generative models to learn the distribution of normal images, which is later used to identify potential anomalous regions derived from errors on the reconstructed images. However,…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
Entropy is critically examined as a fundamental concept in contemporary science and informatics. Although the typical Shannon entropy provides a proper framework for describing the canonical ensemble, it fails to represent adequately the…
The efficiency of microscopic heat engines in a thermally heterogenous environment is considered. We show that, as a consequence of the recently discovered entropic anomaly, quasi-static engines, whose efficiency is maximal in a fluid at…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
By generalizing the density matrix to a transition matrix between two states, represented as $|\phi\rangle$ and $|\psi\rangle$, one can define the pseudoentropy analogous to the entanglement entropy. In this paper, we establish an operator…
A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and…
This work presents a method for information fusion in source localization applications. The method utilizes the concept of optimal mass transport in order to construct estimates of the spatial spectrum using a convex barycenter formulation.…
We study the Shannon entropy of the cluster size distribution in classical as well as explosive percolation, in order to estimate the uncertainty in the sizes of randomly chosen clusters. At the critical point the cluster size distribution…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…
In the estimation theory context, we generalize the notion of Shannon's entropy power to the R\'{e}nyi-entropy setting. This not only allows to find new estimation inequalities, such as the R\'{e}nyi-entropy based De Bruijn identity,…
We introduce a simple geometrical construction similar to covariant holographic entanglement entropy but with the addition of a new term proportional to boundary region volume. This new procedure has properties strongly resembling classical…
Recently, in [P. Jizba and J. Korbel, Physica A 444, 2016, 808-827], four generalized Shannon-Khinchin [GSK] axioms have been proposed and a generalized entropy which uniquely satisfies the GSK axioms has been derived. In this comment, we…
Scaling algorithms for entropic transport-type problems have become a very popular numerical method, encompassing Wasserstein barycenters, multi-marginal problems, gradient flows and unbalanced transport. However, a standard implementation…
The paper examines relationships between the Shannon entropy and the $\ell_{\alpha}$-norm for $n$-ary probability vectors, $n \ge 2$. More precisely, we investigate the tight bounds of the $\ell_{\alpha}$-norm with a fixed Shannon entropy,…
In this paper, we analyze the asymptotics of the normalized remaining uncertainty of a source when a compressed or hashed version of it and correlated side-information is observed. For this system, commonly known as Slepian-Wolf source…
Estimating optimal transport (OT) maps (a.k.a. Monge maps) between two measures $P$ and $Q$ is a problem fraught with computational and statistical challenges. A promising approach lies in using the dual potential functions obtained when…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…
We calculate Shannon information entropy of trapped interacting bosons in both the position and momentum spaces, $S_r$ and $S_k$ respectively. The total entropy maintains the fuctional form $S=a + b \ln N$ for repulsive bosons. At the…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…