29,182 research outputs found
Free Energy Approximations for CSMA networks
In this paper we study how to estimate the back-off rates in an idealized
CSMA network consisting of links to achieve a given throughput vector using
free energy approximations. More specifically, we introduce the class of
region-based free energy approximations with clique belief and present a closed
form expression for the back-off rates based on the zero gradient points of the
free energy approximation (in terms of the conflict graph, target throughput
vector and counting numbers). Next we introduce the size clique free
energy approximation as a special case and derive an explicit expression for
the counting numbers, as well as a recursion to compute the back-off rates. We
subsequently show that the size clique approximation coincides with a
Kikuchi free energy approximation and prove that it is exact on chordal
conflict graphs when . As a by-product these results provide us
with an explicit expression of a fixed point of the inverse generalized belief
propagation algorithm for CSMA networks. Using numerical experiments we compare
the accuracy of the novel approximation method with existing methods
Counting solutions from finite samplings
We formulate the solution counting problem within the framework of inverse
Ising problem and use fast belief propagation equations to estimate the entropy
whose value provides an estimate on the true one. We test this idea on both
diluted models (random 2-SAT and 3-SAT problems) and fully-connected model
(binary perceptron), and show that when the constraint density is small, this
estimate can be very close to the true value. The information stored by the
salamander retina under the natural movie stimuli can also be estimated and our
result is consistent with that obtained by Monte Carlo method. Of particular
significance is sizes of other metastable states for this real neuronal network
are predicted.Comment: 9 pages, 4 figures and 1 table, further discussions adde
Nonparametric generalized belief propagation based on pseudo-junction tree for cooperative localization in wireless networks
Non-parametric belief propagation (NBP) is a well-known message passing method for cooperative localization in wireless networks. However, due to the over-counting problem in the networks with loops, NBP’s convergence is not guaranteed, and its estimates are typically less accurate. One solution for this problem is non-parametric generalized belief propagation based on junction tree. However, this method is intractable in large-scale networks due to the high-complexity of the junction tree formation, and the high-dimensionality of the particles. Therefore, in this article, we propose the non-parametric generalized belief propagation based on pseudo-junction tree (NGBP-PJT). The main difference comparing with the standard method is the formation of pseudo-junction tree, which represents the approximated junction tree based on thin graph. In addition, in order to decrease the number of high-dimensional particles, we use more informative importance density function, and reduce the dimensionality of the messages. As by-product, we also propose NBP based on thin graph (NBP-TG), a cheaper variant of NBP, which runs on the same graph as NGBP-PJT. According to our simulation and experimental results, NGBP-PJT method outperforms NBP and NBP-TG in terms of accuracy, computational, and communication cost in reasonably sized networks
Belief propagation in monoidal categories
We discuss a categorical version of the celebrated belief propagation
algorithm. This provides a way to prove that some algorithms which are known or
suspected to be analogous, are actually identical when formulated generically.
It also highlights the computational point of view in monoidal categories.Comment: In Proceedings QPL 2014, arXiv:1412.810
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