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

• URL: http://arxiv.org/abs/2203.03673v4
• Date: Tue, 1 Aug 2023 05:01:34 GMT
• Title: AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generators
• Authors: Wenkai Xu and Gesine Reinert
• Abstract summary: We propose and analyse a novel statistical procedure, coined AgraSSt, to assess the quality of graph generators. 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. 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.
• Score: 10.616967871198689
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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