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# Approximate Inference Using DC Programming For Collective Graphical Models

*Proceedings of the 19th International Conference on Artificial Intelligence and Statistics*, PMLR 51:685-693, 2016.

#### Abstract

Collective graphical models (CGMs) provide a framework for reasoning about a population of independent and identically distributed individuals when only noisy and aggregate observations are given. Previous approaches for inference in CGMs work on a junction-tree representation, thereby highly limiting their scalability. To remedy this, we show how the Bethe entropy approximation naturally arises for the inference problem in CGMs. We reformulate the resulting optimization problem as a difference-of-convex functions program that can capture different types of CGM noise models. Using the concave-convex procedure, we then develop a scalable message-passing algorithm. Empirically, our approach is highly scalable and accurate for large graphs, more than an order-of-magnitude faster than a generic optimization solver, and is guaranteed to converge unlike the previous message-passing approach NLBP that fails in several loopy graphs.