Barrier Frank-Wolfe for marginal inference

Rahul G. Krishnan, Simon Lacoste-Julien, David Sontag

Research output: Contribution to journalConference article

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.

Original languageEnglish (US)
Pages (from-to)532-540
Number of pages9
JournalAdvances in Neural Information Processing Systems
Volume2015-January
StatePublished - Jan 1 2015
Event29th Annual Conference on Neural Information Processing Systems, NIPS 2015 - Montreal, Canada
Duration: Dec 7 2015Dec 12 2015

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ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Krishnan, R. G., Lacoste-Julien, S., & Sontag, D. (2015). Barrier Frank-Wolfe for marginal inference. Advances in Neural Information Processing Systems, 2015-January, 532-540.