We consider the problem of predicting edges in a graph from node attributes in an e-commerce setting. Specifically, given nodes labelled with search query text, we want to predict links to related queries that share products. Experiments with a range of deep neural architectures show that simple feedforward networks with an attention mechanism perform best for learning embeddings. The simplicity of these models allows us to explain the performance of attention. We propose an analytically tractable model of query generation, AttEST, that views both products and the query text as vectors embedded in a latent space. We prove (and empirically validate) that the point-wise mutual information (PMI) matrix of the AttEST query text embeddings displays a low-rank behavior analogous to that observed in word embeddings. This low-rank property allows us to derive a loss function that maximizes the mutual information between related queries which is used to train an attention network to learn query embeddings. This AttEST network beats traditional memory-based LSTM architectures by over 20% on F-1 score. We justify this out-performance by showing that the weights from the attention mechanism correlate strongly with the weights of the best linear unbiased estimator (BLUE) for the product vectors, and conclude that attention plays an important role in variance reduction.
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