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Barrier Frank-Wolfe for Marginal Inference

Rahul G. Krishnan 1, * Simon Lacoste-Julien 2, 3, 4 David Sontag 1 
* Corresponding author
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within the marginal polytope through repeated maximum a posteriori (MAP) calls. This modular structure enables us to leverage black-box MAP solvers (both exact and approximate) for variational inference, and obtains more accurate results than tree-reweighted algorithms that optimize over the local consistency relaxation. Theoretically, we bound the sub-optimality for the proposed algorithm despite the TRW objective having unbounded gradients at the boundary of the marginal polytope. Empirically, we demonstrate the increased quality of results found by tightening the relaxation over the marginal polytope as well as the spanning tree polytope on synthetic and real-world instances.
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Contributor : Simon Lacoste-Julien Connect in order to contact the contributor
Submitted on : Monday, December 28, 2015 - 4:40:56 AM
Last modification on : Friday, November 18, 2022 - 9:25:57 AM

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  • HAL Id : hal-01248674, version 1
  • ARXIV : 1511.02124



Rahul G. Krishnan, Simon Lacoste-Julien, David Sontag. Barrier Frank-Wolfe for Marginal Inference. NIPS 2015 - Advances in Neural Information Processing Systems 28, Dec 2015, Montreal, Canada. ⟨hal-01248674⟩



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