Universal Marginalizer for Amortised Inference and Embedding of Generative Models
This addresses the problem of efficient and reliable inference in large probabilistic graphical models for researchers and practitioners in machine learning, though it appears incremental as it builds on existing techniques.
The authors tackled the computational cost and lack of theoretical guarantees in inference for large-scale probabilistic graphical models by proposing the Universal Marginaliser Importance Sampler (UM-IS), a hybrid method combining deep neural networks with importance sampling, which outperformed sampling-based methods on a large graph with over 1000 nodes.
Probabilistic graphical models are powerful tools which allow us to formalise our knowledge about the world and reason about its inherent uncertainty. There exist a considerable number of methods for performing inference in probabilistic graphical models; however, they can be computationally costly due to significant time burden and/or storage requirements; or they lack theoretical guarantees of convergence and accuracy when applied to large scale graphical models. To this end, we propose the Universal Marginaliser Importance Sampler (UM-IS) -- a hybrid inference scheme that combines the flexibility of a deep neural network trained on samples from the model and inherits the asymptotic guarantees of importance sampling. We show how combining samples drawn from the graphical model with an appropriate masking function allows us to train a single neural network to approximate any of the corresponding conditional marginal distributions, and thus amortise the cost of inference. We also show that the graph embeddings can be applied for tasks such as: clustering, classification and interpretation of relationships between the nodes. Finally, we benchmark the method on a large graph (>1000 nodes), showing that UM-IS outperforms sampling-based methods by a large margin while being computationally efficient.