Related papers: Maximum Entropy on Compact Groups
There has been much interest in generalizing Kesten's criterion for amenability in terms of a random walk to other contexts, such as determining amenability of a deck covering group by the bottom of the spectrum of the Laplacian or entropy…
We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We…
We define a notion of entropy for an infinite family $\mathcal{C}$ of measurable sets in a probability space. We show that the mean ergodic theorem holds uniformly for $\mathcal{C}$ under every ergodic transformation if and only if…
A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to…
New quantitative propagation of chaos results for mean field diffusion are proved via local and global entropy estimates. In the first result we work on the torus and consider singular, divergence free interactions $K\in L^p$, $p>d$. We…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
For the purpose of causal inference we employ a stochastic model of the data generating process, utilizing individual propensity probabilities for the treatment, and also individual and counterfactual prognosis probabilities for the…
When a hadron is probed at high energy, a nontrivial quantum entanglement entropy inside the hadron emerges due to the lack of complete information about the hadron wave function extracted from this measurement. In the high-energy limit,…
Analytic properties of right topological groups have been extensively studied in the compact admissible case (i.e when the group has a dense topological center). This was inspired by the existence of a Haar measure on such groups. In this…
This report presents a very simple algorithm for overlaping community-detection in large graphs under constraints such as the minimum and maximum number of members allowed. The algorithm is based on the simulation of random walks and…
We consider skew extensions of expanding maps by compact Lie groups. For a class of natural invariant measures, we prove an explicit lower bound on the rate of (exponential) mixing involving topological pressure. Proof uses representation…
An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning.…
Homophily -- the tendency of individuals to interact with similar others -- shapes how networks form and function. Yet existing approaches typically collapse homophily to a single scale, either one parameter for the whole network or one per…
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the…
The maximum likelihood strategy to the estimation of group parameters allows to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results…
We present a procedure for the determination of the interaction potential from the knowledge of the radial pair distribution function. The method, realized inside an inverse Monte Carlo simulation scheme, is based on the application of the…