AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generators

TL;DR

AgraSSt introduces a new statistical method using Stein operators and kernel discrepancies to evaluate and interpret the quality of implicit graph generators, with theoretical guarantees and empirical validation.

Contribution

The paper presents AgraSSt, a novel approach for assessing implicit graph generators using Stein operators, providing interpretability and theoretical guarantees.

Findings

Effective in distinguishing between different graph generation models

Provides interpretable feedback for generator training

Works on both synthetic and real-world graphs

Abstract

We propose and analyse a novel statistical procedure, coined AgraSSt, to assess the quality of graph generators that may not be available in explicit form. In particular, AgraSSt can be used to determine whether a learnt graph generating process is capable of generating graphs that resemble a given input graph. Inspired by Stein operators for random graphs, the key idea of AgraSSt is the construction of a kernel discrepancy based on an operator obtained from the graph generator. AgraSSt can provide interpretable criticisms for a graph generator training procedure and help identify reliable sample batches for downstream tasks. Using Stein`s method we give theoretical guarantees for a broad class of random graph models. We provide empirical results on both synthetic input graphs with known graph generation procedures, and real-world input graphs that the state-of-the-art (deep) generative models for graphs are trained on.