Mathematical Programming: Series A and B
Minimum 0-extensions of graph metrics
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STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
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ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
Collective Inference for Extraction MRFs Coupled with Symmetric Clique Potentials
The Journal of Machine Learning Research
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Inference Methods for CRFs with Co-occurrence Statistics
International Journal of Computer Vision
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The problem of obtaining the maximum a posteriori (MAP) estimate of a discrete random field is of fundamental importance in many areas of Computer Science. In this work, we build on the tree reweighted message passing (TRW) framework of (Kolmogorov, 2006; Wainwright et al., 2005). TRW iteratively optimizes the Lagrangian dual of a linear programming relaxation for MAP estimation. We show how the dual formulation of TRW can be extended to include cycle inequalities (Barahona & Mahjoub, 1986) and some recently proposed second order cone (SOC) constraints (Kumar et al., 2007). We propose efficient iterative algorithms for solving the resulting duals. Similar to the method described in (Kolmogorov, 2006), these algorithms are guaranteed to converge. We test our approach on a large set of synthetic data, as well as real data. Our experiments show that the additional constraints (i.e. cycle inequalities and SOC constraints) provide better results in cases where the TRW framework fails (namely MAP estimation for non-submodular energy functions).