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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.
Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph representat
In this work, we propose to train a graph neural network via resampling from a graphon estimate obtained from the underlying network data. More specifically, the graphon or the link probability matrix of the underlying network is first obtained from
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing
How can we find the right graph for semi-supervised learning? In real world applications, the choice of which edges to use for computation is the first step in any graph learning process. Interestingly, there are often many types of similarity availa
Graph neural networks (GNNs) have been demonstrated to be powerful in modeling graph-structured data. However, training GNNs usually requires abundant task-specific labeled data, which is often arduously expensive to obtain. One effective way to redu