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Probabilistic graphical models are powerful tools which allow us to formaliseour knowledge about the world and reason about its inherent uncertainty. Thereexist a considerable number of methods for performing inference inprobabilistic graphical models; however, they can be computationally costly dueto significant time burden and/or storage requirements; or they lacktheoretical guarantees of convergence and accuracy when applied to large scalegraphical models. To this end, we propose the Universal Marginaliser ImportanceSampler (UM-IS) -- a hybrid inference scheme that combines the flexibility of adeep neural network trained on samples from the model and inherits theasymptotic guarantees of importance sampling. We show how combining samplesdrawn from the graphical model with an appropriate masking function allows usto train a single neural network to approximate any of the correspondingconditional marginal distributions, and thus amortise the cost of inference. Wealso show that the graph embeddings can be applied for tasks such as:clustering, classification and interpretation of relationships between thenodes. Finally, we benchmark the method on a large graph (>1000 nodes), showingthat UM-IS outperforms sampling-based methods by a large margin while beingcomputationally efficient.

Universal Marginalizer for Amortised Inference and Embedding of Generative Models