## An Iterated LP Approach to the Exact Computation of the Partition Function in General Markov Random Field Models

**Authors:** Ikhlef Bechar

In a recent paper (I. Bechar, 2017), we have shown that one may efficiently compute the marginals of a general higher-order Markov random field (MRF) model with respect to an arbitrary collection of point subsets by solving a single linear program. Therefore, in this paper, we build on such a work for showing that the partition function of a general higher-order MRF model may, in turn, be computed both in an exact and efficient way, by iteratively solving, at most, $n$ linear programs, with $n$ standing for the number of nodes in the graph representation of a MRF model. This is, first, achieved by establishing a recursive formula between the partition function of a given MRF model and the one of another (one-node smaller) MRF model resulting from the pruning of any of the nodes of the graph of the former. Then, we show that the problem amounts to solving successive and increasingly simpler MRF marginal inference problems, and thus, one may use the approach developed in (I. Bechar, 2017) for solving such MRF marginal inference problems.

**Comments:** 21 Pages. improved version

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### Submission history

[v1] 2017-09-18 15:55:53

[v2] 2017-09-20 07:40:31

**Unique-IP document downloads:** 15 times

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