6,460 research outputs found
Capacity-achieving ensembles for the binary erasure channel with bounded complexity
We present two sequences of ensembles of non-systematic irregular
repeat-accumulate codes which asymptotically (as their block length tends to
infinity) achieve capacity on the binary erasure channel (BEC) with bounded
complexity per information bit. This is in contrast to all previous
constructions of capacity-achieving sequences of ensembles whose complexity
grows at least like the log of the inverse of the gap (in rate) to capacity.
The new bounded complexity result is achieved by puncturing bits, and allowing
in this way a sufficient number of state nodes in the Tanner graph representing
the codes. We also derive an information-theoretic lower bound on the decoding
complexity of randomly punctured codes on graphs. The bound holds for every
memoryless binary-input output-symmetric channel and is refined for the BEC.Comment: 47 pages, 9 figures. Submitted to IEEE Transactions on Information
Theor
Cut Size Statistics of Graph Bisection Heuristics
We investigate the statistical properties of cut sizes generated by heuristic
algorithms which solve approximately the graph bisection problem. On an
ensemble of sparse random graphs, we find empirically that the distribution of
the cut sizes found by ``local'' algorithms becomes peaked as the number of
vertices in the graphs becomes large. Evidence is given that this distribution
tends towards a Gaussian whose mean and variance scales linearly with the
number of vertices of the graphs. Given the distribution of cut sizes
associated with each heuristic, we provide a ranking procedure which takes into
account both the quality of the solutions and the speed of the algorithms. This
procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also
available at http://ipnweb.in2p3.fr/~martin
Markov Network Structure Learning via Ensemble-of-Forests Models
Real world systems typically feature a variety of different dependency types
and topologies that complicate model selection for probabilistic graphical
models. We introduce the ensemble-of-forests model, a generalization of the
ensemble-of-trees model. Our model enables structure learning of Markov random
fields (MRF) with multiple connected components and arbitrary potentials. We
present two approximate inference techniques for this model and demonstrate
their performance on synthetic data. Our results suggest that the
ensemble-of-forests approach can accurately recover sparse, possibly
disconnected MRF topologies, even in presence of non-Gaussian dependencies
and/or low sample size. We applied the ensemble-of-forests model to learn the
structure of perturbed signaling networks of immune cells and found that these
frequently exhibit non-Gaussian dependencies with disconnected MRF topologies.
In summary, we expect that the ensemble-of-forests model will enable MRF
structure learning in other high dimensional real world settings that are
governed by non-trivial dependencies.Comment: 13 pages, 6 figure
Iterative graph cuts for image segmentation with a nonlinear statistical shape prior
Shape-based regularization has proven to be a useful method for delineating
objects within noisy images where one has prior knowledge of the shape of the
targeted object. When a collection of possible shapes is available, the
specification of a shape prior using kernel density estimation is a natural
technique. Unfortunately, energy functionals arising from kernel density
estimation are of a form that makes them impossible to directly minimize using
efficient optimization algorithms such as graph cuts. Our main contribution is
to show how one may recast the energy functional into a form that is
minimizable iteratively and efficiently using graph cuts.Comment: Revision submitted to JMIV (02/24/13
- …