Evaluating Graph Generative Models with Graph Kernels: What Structural Characteristics Are Captured?
Abstract: For many practical problems, it is important to measure similarity between graphs. This can be done via graph kernels. One particular application where the choice of a graph kernel is essential is assessing the quality of graph generative models. However, despite the vast number of graph kernels available in the literature, only basic kernels are usually considered for generative model evaluation. In this paper, we fill this gap and analyze how different graph kernels perform as an ingredient in the pipeline of generative model performance evaluation. To conduct a detailed analysis, we propose a framework for comparing graph kernels in terms of which high-level structural properties they are sensitive to: heterogeneity of degree distribution, the presence of community structure, the presence of latent geometry, and others. For this, we design continuous transitions between random graph models that affect a particular property and measure which graph kernel is sensitive to the corresponding change. We show that using such diverse models with the corresponding transitions is crucial for evaluation: many kernels can successfully capture some properties and fail on others. We also found some well-known kernels that show good performance in our experiments but have been previously overlooked in the literature on evaluating graph generative models.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Kenta_Oono1
Submission Number: 3343
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