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Probabilistic Graphical Model (PGM) Perspective on GNNs
Graph Neural Networks (GNNs) can be theoretically motivated by their connections to variational inference in probabilistic graphical models (PGMs). From this probabilistic perspective, the embeddings for each node are viewed as latent variables to be inferred. Assuming the graph structure and the input node features are observed, the goal is to infer the underlying latent variables that can explain this observed data. Consequently, the message passing operations underlying GNNs can be viewed as a neural network analogue of message passing algorithms commonly used for variational inference to infer distributions over these latent variables.
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Data Science