Supervised Learning of a Generative Model for Edge-Weighted Graphs

Abstract

This paper addresses the problem of learning archetypal structural models from examples. To this end we define a generative model for graphs where the distribution of observed nodes and edges is governed by a set of independent Bernoulli trials with parameters to be estimated from data in a situation where the correspondences between the nodes in the data graphs and the nodes in the model are not not known ab initio and must be estimated from local structure. This results in an EM-like approach where we alternate the estimation of the node correspondences with the estimation of the model parameters. Parameter estimation and model order selection is addressed within a Minimum Message Length (MML) framework.

Heat Flow-Thermodynamic Depth Complexity in Directed Networks

“…Information theory [1] provides principled approaches to the analysis complexity that include minimum description length (MDL) and minimum message length (MML) which allow us to find the model that parsimoniously describes vectorial data. However, the latter principles have not been incorporated to the graph domain until recently (see [2] for trees and [3] for edge-weighted undirected graphs). In fact, the intersection between structural pattern recognition and complex networks has proved to be fruitful and has inspired several interesting measures of graph complexity.…”