36,537 research outputs found
Scalable Semidefinite Relaxation for Maximum A Posterior Estimation
Maximum a posteriori (MAP) inference over discrete Markov random fields is a
fundamental task spanning a wide spectrum of real-world applications, which is
known to be NP-hard for general graphs. In this paper, we propose a novel
semidefinite relaxation formulation (referred to as SDR) to estimate the MAP
assignment. Algorithmically, we develop an accelerated variant of the
alternating direction method of multipliers (referred to as SDPAD-LR) that can
effectively exploit the special structure of the new relaxation. Encouragingly,
the proposed procedure allows solving SDR for large-scale problems, e.g.,
problems on a grid graph comprising hundreds of thousands of variables with
multiple states per node. Compared with prior SDP solvers, SDPAD-LR is capable
of attaining comparable accuracy while exhibiting remarkably improved
scalability, in contrast to the commonly held belief that semidefinite
relaxation can only been applied on small-scale MRF problems. We have evaluated
the performance of SDR on various benchmark datasets including OPENGM2 and PIC
in terms of both the quality of the solutions and computation time.
Experimental results demonstrate that for a broad class of problems, SDPAD-LR
outperforms state-of-the-art algorithms in producing better MAP assignment in
an efficient manner.Comment: accepted to International Conference on Machine Learning (ICML 2014
A Compact Linear Programming Relaxation for Binary Sub-modular MRF
We propose a novel compact linear programming (LP) relaxation for binary
sub-modular MRF in the context of object segmentation. Our model is obtained by
linearizing an -norm derived from the quadratic programming (QP) form of
the MRF energy. The resultant LP model contains significantly fewer variables
and constraints compared to the conventional LP relaxation of the MRF energy.
In addition, unlike QP which can produce ambiguous labels, our model can be
viewed as a quasi-total-variation minimization problem, and it can therefore
preserve the discontinuities in the labels. We further establish a relaxation
bound between our LP model and the conventional LP model. In the experiments,
we demonstrate our method for the task of interactive object segmentation. Our
LP model outperforms QP when converting the continuous labels to binary labels
using different threshold values on the entire Oxford interactive segmentation
dataset. The computational complexity of our LP is of the same order as that of
the QP, and it is significantly lower than the conventional LP relaxation
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