Inference and Sampling of $K_33$free Ising Models
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:39633972, 2019.
Abstract
We call an Ising model tractable when it is possible to compute its partition function value (statistical inference) in polynomial time. The tractability also implies an ability to sample configurations of this model in polynomial time. The notion of tractability extends the basic case of planar zerofield Ising models. Our starting point is to describe algorithms for the basic case, computing partition function and sampling efficiently. Then, we extend our tractable inference and sampling algorithms to models whose triconnected components are either planar or graphs of $O(1)$ size. In particular, it results in a polynomialtime inference and sampling algorithms for $K_{33}$ (minor)free topologies of zerofield Ising models—a generalization of planar graphs with a potentially unbounded genus.
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