# Efficient Exact Inference in Planar Ising Models

@inproceedings{Schraudolph2008EfficientEI, title={Efficient Exact Inference in Planar Ising Models}, author={Nicol N. Schraudolph and Dmitry Kamenetsky}, booktitle={NIPS}, year={2008} }

We give polynomial-time algorithms for the exact computation of lowest-energy states, worst margin violators, partition functions, and marginals in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it does not impose any submodularity constraints; instead we require planarity to establish a correspondence with perfect matchings in an expanded dual graph. Maximum-margin parameter estimation for a boundary… Expand

#### 81 Citations

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The key to the construction is the complementary correspondence between graph cuts of the model graph and perfect matchings of its expanded dual, and it is shown that the exact algorithms are effective and efficient on a number of real-world machine learning problems. Expand

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A simple, efficient, algorithm that infers the ground truth with optimal Hamming error has optimal sample complexity and implies recovery results for all connected graphs and the power of this method is shown in several examples including hypergrids, ring lattices, and the Newman-Watts model for small world graphs. Expand

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We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components along with subsets of at most three vertices… Expand

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- 2016

We revisit classical bounds of M. E. Fisher on the ferromagnetic Ising model, and show how to efficiently use them on an arbitrary given graph to rigorously upper-bound the partition function,… Expand

Dynamic Planar-Cuts : Efficient Computation of Min-Marginals for OuterPlanar MRFs

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