Related papers: Information Geometry of Random Matrix Models
The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of…
In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n^{1/2} X_n\tilde D_n^{1/2} +A_n$, as the…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,... All these topics share certain relations, called "loop equations" or…
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of…
In a previous paper (C. Cafaro et al., 2012), we compared an uncorrelated 3D Gaussian statistical model to an uncorrelated 2D Gaussian statistical model obtained from the former model by introducing a constraint that resembles the quantum…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011)…
Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the Authors and collaborators during the last decade…
We model the transmission of a message on the complete graph with n vertices and limited resources. The vertices of the graph represent servers that may broadcast the message at random. Each server has a random emission capital that…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies…
We consider a prototypical problem of Bayesian inference for a structured spiked model: a low-rank signal is corrupted by additive noise. While both information-theoretic and algorithmic limits are well understood when the noise is a…
We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $\beta$-model for random graphs by…
In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of…
We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold)…
In this paper, new methodology -- direct approach -- for the determination of the attainable CR type bound of the pure state model, is proposed and successfully applied to the wide variety of pure state models, for example, the…