Related papers: Maximum-entropy inference and inverse continuity o…
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…
We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an…
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…
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…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
The Boltzmann-Wallis-Jaynes' multiplicity argument is taken up and elaborated. MaxEnt is proved and demonstrated to be just an asymptotic case of looking for such a vector of absolute frequencies in a feasible set, which has maximal…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for two cases: 1) any operator monotone decreasing function and full rank mixed qubit or classical states; 2) a large class of…
The Principle of Insufficient Reason (PIR) assigns equal probabilities to each alternative of a random experiment whenever there is no reason to prefer one over the other. The Maximum Entropy Principle (MaxEnt) generalizes PIR to the case…
We study the pointwise perturbations of countable Markov maps with infinitely many inverse branches and establish the following continuity theorem: Let $T_k$ and $T$ be expanding countable Markov maps such that the inverse branches of $T_k$…
The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
Maximum likelihood estimation is a valuable tool often applied to inverse problems in quantum theory. Estimation from small data sets can, however, have non unique solutions. We discuss this problem and propose to use Jaynes maximum entropy…
In connection with the Entropy Conjecture it is known that the topological entropy of a continuous graph map is bounded from below by the spectral radius of the induced map on the first homology group. We show that in the case of a…
In this paper we study the polynomial entropy of homeomorphism on compact metric space. We construct a homeomorphism on a compact metric space with vanishing polynomial entropy that it is not equicontinuous. Also we give examples with…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…