Learning Graphon Autoencoders for Generative Graph Modeling

Abstract

Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called \textit{graphon autoencoder} to build an interpretable and scalable graph generative model. This framework treats observed graphs as induced graphons in functional space and derives their latent representations by an encoder that aggregates Chebshev graphon filters. A linear graphon factorization model works as a decoder, leveraging the latent representations to reconstruct the induced graphons (and the corresponding observed graphs). We develop an efficient learning algorithm to learn the encoder and the decoder, minimizing the Wasserstein distance between the model and data distributions. This algorithm takes the KL divergence of the graph distributions conditioned on different graphons as the underlying distance and leads to a reward-augmented maximum likelihood estimation. The graphon autoencoder provides a new paradigm to represent and generate graphs, which has good generalizability and transferability.

References in corpus (15)

• Adam: A Method for Stochastic Optimization
• Variational Graph Auto-Encoders
• graph2vec: Learning Distributed Representations of Graphs
• Matrix estimation by Universal Singular Value Thresholding
• TUDataset: A collection of benchmark datasets for learning with graphs
• GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation
• Subgraph Matching Kernels for Attributed Graphs
• Optimal Transport for structured data with application on graphs
• The Multiscale Laplacian Graph Kernel
• Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance
• Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model
• A Consistent Histogram Estimator for Exchangeable Graph Models
• A simple yet effective baseline for non-attributed graph classification
• Graphon Filters: Graph Signal Processing in the Limit
• Scalable Deep Generative Modeling for Sparse Graphs