10,230 research outputs found
Efficient Semidefinite Branch-and-Cut for MAP-MRF Inference
We propose a Branch-and-Cut (B&C) method for solving general MAP-MRF
inference problems. The core of our method is a very efficient bounding
procedure, which combines scalable semidefinite programming (SDP) and a
cutting-plane method for seeking violated constraints. In order to further
speed up the computation, several strategies have been exploited, including
model reduction, warm start and removal of inactive constraints.
We analyze the performance of the proposed method under different settings,
and demonstrate that our method either outperforms or performs on par with
state-of-the-art approaches. Especially when the connectivities are dense or
when the relative magnitudes of the unary costs are low, we achieve the best
reported results. Experiments show that the proposed algorithm achieves better
approximation than the state-of-the-art methods within a variety of time
budgets on challenging non-submodular MAP-MRF inference problems.Comment: 21 page
A Novel Convex Relaxation for Non-Binary Discrete Tomography
We present a novel convex relaxation and a corresponding inference algorithm
for the non-binary discrete tomography problem, that is, reconstructing
discrete-valued images from few linear measurements. In contrast to state of
the art approaches that split the problem into a continuous reconstruction
problem for the linear measurement constraints and a discrete labeling problem
to enforce discrete-valued reconstructions, we propose a joint formulation that
addresses both problems simultaneously, resulting in a tighter convex
relaxation. For this purpose a constrained graphical model is set up and
evaluated using a novel relaxation optimized by dual decomposition. We evaluate
our approach experimentally and show superior solutions both mathematically
(tighter relaxation) and experimentally in comparison to previously proposed
relaxations
Covariant velocity and density perturbations in quasi-Newtonian cosmologies
Recently a covariant approach to cold matter universes in the zero-shear
hypersurfaces (or longitudinal) gauge has been developed. This approach reveals
the existence of an integrability condition, which does not appear in standard
non-covariant treatments. A simple derivation and generalization of the
integrability condition is given, based on showing that the quasi-Newtonian
models are a sub-class of the linearized `silent' models. The solution of the
integrability condition implies a propagation equation for the acceleration. It
is shown how the velocity and density perturbations are then obtained via this
propagation equation. The density perturbations acquire a small
relative-velocity correction on all scales, arising from the fully covariant
general relativistic analysis.Comment: 11 pages Revtex; to appear Phys. Rev.
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