Goodness-of-Fit of Attributed Probabilistic Graph Generative Models

TL;DR

This paper introduces a method to evaluate how well probabilistic attributed graph models fit observed data by using a statistical measure, ensuring their structural accuracy.

Contribution

It defines a goodness-of-fit criterion for attributed probabilistic graph models based on the mean square contingency coefficient and provides a procedure for assessment.

Findings

The proposed method effectively assesses model fit for various graph types.

It ensures minimal discrepancy in the mean square contingency coefficient with high probability.

The approach verifies the representation capability of probabilistic graph models.

Abstract

Probabilistic generative models of graphs are important tools that enable representation and sampling. Many recent works have created probabilistic models of graphs that are capable of representing not only entity interactions but also their attributes. However, given a generative model of random attributed graph(s), the general conditions that establish goodness of fit are not clear a-priori. In this paper, we define goodness of fit in terms of the mean square contingency coefficient for random binary networks. For this statistic, we outline a procedure for assessing the quality of the structure of a learned attributed graph by ensuring that the discrepancy of the mean square contingency coefficient (constant, or random) is minimal with high probability. We apply these criteria to verify the representation capability of a probabilistic generative model for various popular types of graph models.