3,568 research outputs found
Bethe Projections for Non-Local Inference
Many inference problems in structured prediction are naturally solved by
augmenting a tractable dependency structure with complex, non-local auxiliary
objectives. This includes the mean field family of variational inference
algorithms, soft- or hard-constrained inference using Lagrangian relaxation or
linear programming, collective graphical models, and forms of semi-supervised
learning such as posterior regularization. We present a method to
discriminatively learn broad families of inference objectives, capturing
powerful non-local statistics of the latent variables, while maintaining
tractable and provably fast inference using non-Euclidean projected gradient
descent with a distance-generating function given by the Bethe entropy. We
demonstrate the performance and flexibility of our method by (1) extracting
structured citations from research papers by learning soft global constraints,
(2) achieving state-of-the-art results on a widely-used handwriting recognition
task using a novel learned non-convex inference procedure, and (3) providing a
fast and highly scalable algorithm for the challenging problem of inference in
a collective graphical model applied to bird migration.Comment: minor bug fix to appendix. appeared in UAI 201
Barrier Frank-Wolfe for Marginal Inference
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.Comment: 25 pages, 12 figures, To appear in Neural Information Processing
Systems (NIPS) 2015, Corrected reference and cleaned up bibliograph
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