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Incremental Clustering and Expansion for Faster Optimal Planning in Decentralized POMDPs
, 2013
"... This article presents the stateoftheart in optimal solution methods for decentralized partially observable Markov decision processes (DecPOMDPs), which are general models for collaborative multiagent planning under uncertainty. Building off the generalized multiagent A * (GMAA*) algorithm, which ..."
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Cited by 19 (12 self)
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This article presents the stateoftheart in optimal solution methods for decentralized partially observable Markov decision processes (DecPOMDPs), which are general models for collaborative multiagent planning under uncertainty. Building off the generalized multiagent A * (GMAA*) algorithm, which reduces the problem to a tree of oneshot collaborative Bayesian games (CBGs), we describe several advances that greatly expand the range of DecPOMDPs that can be solved optimally. First, we introduce lossless incremental clustering of the CBGs solved by GMAA*, which achieves exponential speedups without sacrificing optimality. Second, we introduce incremental expansion of nodes in the GMAA * search tree, which avoids the need to expand all children, the number of which is in the worst case doubly exponential in the node’s depth. This is particularly beneficial when little clustering is possible. In addition, we introduce new hybrid heuristic representations that are more compact and thereby enable the solution of larger DecPOMDPs. We provide theoretical guarantees that, when a suitable heuristic is used, both incremental clustering and incremental expansion yield algorithms that are both complete and search equivalent. Finally, we present extensive empirical results demonstrating that GMAA*ICE, an algorithm that synthesizes these advances, can optimally solve DecPOMDPs of unprecedented size.
An Efficient MessagePassing Algorithm for the MBest MAP Problem
"... Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model – known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable ..."
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Cited by 7 (3 self)
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Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model – known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable solutions – known as the MBest MAP problem. In this paper, we propose an efficient messagepassing based algorithm for solving the MBest MAP problem. Specifically, our algorithm solves the recently proposed Linear Programming (LP) formulation of MBest MAP [7], while being orders of magnitude faster than a generic LPsolver. Our approach relies on studying a particular partial Lagrangian relaxation of the MBest MAP LP which exposes a natural combinatorial structure of the problem that we exploit. 1
A System for Exact and Approximate Genetic Linkage Analysis of SNP Data in Large Pedigrees
, 2012
"... The wide availability of dense single nucleotide polymorphism (SNP) data imposes computational bottlenecks on genetic linkage analysis of large pedigrees exceeding the capabilities of contemporary computers. Here we report SuperlinkOnline SNP, a new strong system for analysis of SNP data on large p ..."
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Cited by 1 (0 self)
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The wide availability of dense single nucleotide polymorphism (SNP) data imposes computational bottlenecks on genetic linkage analysis of large pedigrees exceeding the capabilities of contemporary computers. Here we report SuperlinkOnline SNP, a new strong system for analysis of SNP data on large pedigrees. SuperlinkOnline SNP provides geneticists a collection of highly integrated services, including sifting of erroneous data, SNP clustering, exact and approximate LOD calculations, and maximum likelihood haplotyping. This integrated system better facilitates a workflow towards easier pinpointing of disease genes. Computations performed by SuperlinkOnline SNP are automatically parallelized using novel paradigms, and executed on unlimited number of private or public CPUs. One novel service is high scale approximate Markov ChainMonte Carlo (MCMC) analysis. The accuracy of the results is reliably estimated by running the same computation on multiple CPUs and evaluating the GelmanRubin Score to discard unreliable results. Another service within the workflow is a novel parallelized exact algorithm for inferring maximum likelihood haplotyping. The reported system enables genetic analyses that were previously infeasible. Genetic linkage analysis is a statistical method for locating diseasesusceptibility genes. Existing computer packages that perform exact genetic linkage analysis, such as Merlin, 1 Allegro, 2 GENEHUNTER, 3 Superlink4 and Vitesse5 use either the
Global Sensitivity Analysis for MAP Inference in Graphical Models
"... We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contri ..."
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We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios. 1