443 research outputs found
Getting Feasible Variable Estimates From Infeasible Ones: MRF Local Polytope Study
This paper proposes a method for construction of approximate feasible primal
solutions from dual ones for large-scale optimization problems possessing
certain separability properties. Whereas infeasible primal estimates can
typically be produced from (sub-)gradients of the dual function, it is often
not easy to project them to the primal feasible set, since the projection
itself has a complexity comparable to the complexity of the initial problem. We
propose an alternative efficient method to obtain feasibility and show that its
properties influencing the convergence to the optimum are similar to the
properties of the Euclidean projection. We apply our method to the local
polytope relaxation of inference problems for Markov Random Fields and
demonstrate its superiority over existing methods.Comment: 20 page, 4 figure
MAP inference via Block-Coordinate Frank-Wolfe Algorithm
We present a new proximal bundle method for Maximum-A-Posteriori (MAP)
inference in structured energy minimization problems. The method optimizes a
Lagrangean relaxation of the original energy minimization problem using a multi
plane block-coordinate Frank-Wolfe method that takes advantage of the specific
structure of the Lagrangean decomposition. We show empirically that our method
outperforms state-of-the-art Lagrangean decomposition based algorithms on some
challenging Markov Random Field, multi-label discrete tomography and graph
matching problems
Generalized sequential tree-reweighted message passing
This paper addresses the problem of approximate MAP-MRF inference in general
graphical models. Following [36], we consider a family of linear programming
relaxations of the problem where each relaxation is specified by a set of
nested pairs of factors for which the marginalization constraint needs to be
enforced. We develop a generalization of the TRW-S algorithm [9] for this
problem, where we use a decomposition into junction chains, monotonic w.r.t.
some ordering on the nodes. This generalizes the monotonic chains in [9] in a
natural way. We also show how to deal with nested factors in an efficient way.
Experiments show an improvement over min-sum diffusion, MPLP and subgradient
ascent algorithms on a number of computer vision and natural language
processing problems
The Lazy Flipper: MAP Inference in Higher-Order Graphical Models by Depth-limited Exhaustive Search
This article presents a new search algorithm for the NP-hard problem of
optimizing functions of binary variables that decompose according to a
graphical model. It can be applied to models of any order and structure. The
main novelty is a technique to constrain the search space based on the topology
of the model. When pursued to the full search depth, the algorithm is
guaranteed to converge to a global optimum, passing through a series of
monotonously improving local optima that are guaranteed to be optimal within a
given and increasing Hamming distance. For a search depth of 1, it specializes
to Iterated Conditional Modes. Between these extremes, a useful tradeoff
between approximation quality and runtime is established. Experiments on models
derived from both illustrative and real problems show that approximations found
with limited search depth match or improve those obtained by state-of-the-art
methods based on message passing and linear programming.Comment: C++ Source Code available from
http://hci.iwr.uni-heidelberg.de/software.ph
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