We propose MHM-GNN, an inductive unsupervised graph representation approach that combines jointk-node representations with energy-based models (hypergraph Markov networks) and GNNs.

A.2 Proof of Theorem 1 To prove Theorem 1, we assume that G Proof of Lemma 1. Let's first rewrite Equation (4) as null null By Lemma 1, linearity of expectation and knowing that each RWT is independent from the other tours by the Strong Markov Property, Theorem 1 holds. MHM-GNN can recover edge-based models where representations don't use graph-wide However, on Rent the Runway we see the raw features achieving the highest performance. That is, structural information does not seem to be relevant to this specific task. All hyperparameters were chosen to minimize training loss. For k = 5, we used a minibatch of size 5 in all datasets.

Figure 1: The proposed unsupervised graph representation using motif compositions.

Existing Graph Neural Network (GNN) methods that learn inductive unsupervised graph representations focus on learning node and edge representations by predicting observed edges in the graph. Although such approaches have shown advances in downstream node classification tasks, they are ineffective in jointly representing larger $k$-node sets, $k{>}2$. We propose MHM-GNN, an inductive unsupervised graph representation approach that combines joint $k$-node representations with energy-based models (hypergraph Markov networks) and GNNs. To address the intractability of the loss that arises from this combination, we endow our optimization with a loss upper bound using a finite-sample unbiased Markov Chain Monte Carlo estimator. Our experiments show that the unsupervised MHM-GNN representations of MHM-GNN produce better unsupervised representations than existing approaches from the literature.