Related papers: Mean field information Hessian matrices on graphs

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…

This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…

This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…

We introduce the notion of information ratio $\text{Ir}(H/G)$ between two (simple, undirected) graphs $G$ and $H$, defined as the supremum of ratios $k/n$ such that there exists a mapping between the strong products $G^k$ to $H^n$ that…

We introduce an information-theoretic quantity with similar properties to mutual information that can be estimated from data without making explicit assumptions on the underlying distribution. This quantity is based on a recently proposed…

We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…

The zero temperature relaxational dynamics of a particle in a short range correlated random potential is addressed. We derive a set of "two-times" mean-field dynamical equations, accounting for a possible mean displacement of the particle…

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…

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…

Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropies have been proposed in brain network analysis. However, they are less…

We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of…

Random factor graphs provide a powerful framework for the study of inference problems such as decoding problems or the stochastic block model. Information-theoretically the key quantity of interest is the mutual information between the…

We introduce and study Laplacians on a finite metric graph endowed with generalized densities, that is, measures of finite mass. One important motivation is that this setting provides a common framework for several interesting classes of…

We give inequalities relating the eigenvalues of the adjacency matrix and the Laplacian of a graph, and its minimum and maximum degrees. The results are applied to derive new conditions for quasi-randomness of graphs.

Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…

We present tree extraction in 3D images as a graph refinement task, of obtaining a subgraph from an over-complete input graph. To this end, we formulate an approximate Bayesian inference framework on undirected graphs using mean field…

We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…

Transport-based techniques for signal and data analysis have received increased attention recently. Given their abilities to provide accurate generative models for signal intensities and other data distributions, they have been used in a…

Lott-Sturm-Villani theory of curvature on geodesic spaces has been extended to discrete graph spaces by C. L{\'e}onard by replacing W2-Wasserstein geodesics by Schr{\"o}odinger bridges in the definition of entropic curvature [23, 25, 24].…

Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by adding the Fisher Information as the regularizer, we relate the…