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ABSTRACT: We propose an approach to lifted approximate inference for first-order
probabilistic models, such as Markov logic networks. It is based on performing
exact lifted inference in a simplified first-order model, which is found by
relaxing first-order constraints, and then compensating for the relaxation.
These simplified models can be incrementally improved by carefully recovering
constraints that have been relaxed, also at the first-order level. This leads
to a spectrum of approximations, with lifted belief propagation on one end, and
exact lifted inference on the other. We discuss how relaxation, compensation,
and recovery can be performed, all at the firstorder level, and show
empirically that our approach substantially improves on the approximations of
both propositional solvers and lifted belief propagation.
10/2012;
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ABSTRACT: EDML is a recently proposed algorithm for learning MAP parameters in Bayesian
networks. In this paper, we present a number of new advances and insights on
the EDML algorithm. First, we provide the multivalued extension of EDML,
originally proposed for Bayesian networks over binary variables. Next, we
identify a simplified characterization of EDML that further implies a simple
fixed-point algorithm for the convex optimization problem that underlies it.
This characterization further reveals a connection between EDML and EM: a fixed
point of EDML is a fixed point of EM, and vice versa. We thus identify also a
new characterization of EM fixed points, but in the semantics of EDML. Finally,
we propose a hybrid EDML/EM algorithm that takes advantage of the improved
empirical convergence behavior of EDML, while maintaining the monotonic
improvement property of EM.
10/2012;
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ABSTRACT: We consider the problem of deleting edges from a Bayesian network for the
purpose of simplifying models in probabilistic inference. In particular, we
propose a new method for deleting network edges, which is based on the evidence
at hand. We provide some interesting bounds on the KL-divergence between
original and approximate networks, which highlight the impact of given evidence
on the quality of approximation and shed some light on good and bad candidates
for edge deletion. We finally demonstrate empirically the promise of the
proposed edge deletion technique as a basis for approximate inference.
07/2012;
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ABSTRACT: We consider in this paper the formulation of approximate inference in
Bayesian networks as a problem of exact inference on an approximate network
that results from deleting edges (to reduce treewidth). We have shown in
earlier work that deleting edges calls for introducing auxiliary network
parameters to compensate for lost dependencies, and proposed intuitive
conditions for determining these parameters. We have also shown that our method
corresponds to IBP when enough edges are deleted to yield a polytree, and
corresponds to some generalizations of IBP when fewer edges are deleted. In
this paper, we propose a different criteria for determining auxiliary
parameters based on optimizing the KL-divergence between the original and
approximate networks. We discuss the relationship between the two methods for
selecting parameters, shedding new light on IBP and its generalizations. We
also discuss the application of our new method to approximating inference
problems which are exponential in constrained treewidth, including MAP and
nonmyopic value of information.
06/2012;
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ABSTRACT: We formulate in this paper the mini-bucket algorithm for approximate
inference in terms of exact inference on an approximate model produced by
splitting nodes in a Bayesian network. The new formulation leads to a number of
theoretical and practical implications. First, we show that branchand- bound
search algorithms that use minibucket bounds may operate in a drastically
reduced search space. Second, we show that the proposed formulation inspires
new minibucket heuristics and allows us to analyze existing heuristics from a
new perspective. Finally, we show that this new formulation allows mini-bucket
approximations to benefit from recent advances in exact inference, allowing one
to significantly increase the reach of these approximations.
06/2012;
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ABSTRACT: We propose an approach for approximating the partition function which is
based on two steps: (1) computing the partition function of a simplified model
which is obtained by deleting model edges, and (2) rectifying the result by
applying an edge-by-edge correction. The approach leads to an intuitive
framework in which one can trade-off the quality of an approximation with the
complexity of computing it. It also includes the Bethe free energy
approximation as a degenerate case. We develop the approach theoretically in
this paper and provide a number of empirical results that reveal its practical
utility.
06/2012;
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CoRR. 01/2012; abs/1202.3709.
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UAI 2011, Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, Barcelona, Spain, July 14-17, 2011; 01/2011
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ABSTRACT: MOTIVATION: Haplotype inference is an important step for many types of analyses of genetic variation in the human genome. Traditional approaches for obtaining haplotypes involve collecting genotype information from a population of individuals and then applying a haplotype inference algorithm. The development of high-throughput sequencing technologies allows for an alternative strategy to obtain haplotypes by combining sequence fragments. The problem of 'haplotype assembly' is the problem of assembling the two haplotypes for a chromosome given the collection of such fragments, or reads, and their locations in the haplotypes, which are pre-determined by mapping the reads to a reference genome. Errors in reads significantly increase the difficulty of the problem and it has been shown that the problem is NP-hard even for reads of length 2. Existing greedy and stochastic algorithms are not guaranteed to find the optimal solutions for the haplotype assembly problem. RESULTS: In this article, we proposed a dynamic programming algorithm that is able to assemble the haplotypes optimally with time complexity O(m x 2(k) x n), where m is the number of reads, k is the length of the longest read and n is the total number of SNPs in the haplotypes. We also reduce the haplotype assembly problem into the maximum satisfiability problem that can often be solved optimally even when k is large. Taking advantage of the efficiency of our algorithm, we perform simulation experiments demonstrating that the assembly of haplotypes using reads of length typical of the current sequencing technologies is not practical. However, we demonstrate that the combination of this approach and the traditional haplotype phasing approaches allow us to practically construct haplotypes containing both common and rare variants.
Bioinformatics 06/2010; 26(12):i183-90. · 5.47 Impact Factor
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New Frontiers in Artificial Intelligence - JSAI-isAI 2010 Workshops, LENLS, JURISIN, AMBN, ISS, Tokyo, Japan, November 18-19, 2010, Revised Selected Papers; 01/2010
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Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009. Proceedings of a meeting held 7-10 December 2009, Vancouver, British Columbia, Canada.; 01/2009
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Principles and Practice of Constraint Programming - CP 2009, 15th International Conference, CP 2009, Lisbon, Portugal, September 20-24, 2009, Proceedings; 01/2009
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JSAT. 01/2008; 4:191-217.
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Algorithms in Bioinformatics, 8th International Workshop, WABI 2008, Karlsruhe, Germany, September 15-19, 2008. Proceedings; 01/2008
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Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, July 13-17, 2008; 01/2008
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Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, July 13-17, 2008; 01/2008
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Proceedings, The Twenty-First National Conference on Artificial Intelligence and the Eighteenth Innovative Applications of Artificial Intelligence Conference, July 16-20, 2006, Boston, Massachusetts, USA; 01/2006
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ABSTRACT: We introduce a new perspective on approximations to the maximum a posteriori (MAP) task in probabilistic graphical models, that is based on simplifying a given instance, and then tightening the approximation. First, we start with a structural relaxation of the original model. We then infer from the relaxation its deficien-cies, and compensate for them. This perspective allows us to identify two distinct classes of approximations. First, we find that max-product belief propagation can be viewed as a way to compensate for a relaxation, based on a particular idealized case for exactness. We identify a second approach to compensation that is based on a more refined idealized case, resulting in a new approximation with distinct properties. We go on to propose a new class of algorithms that, starting with a relaxation, iteratively seeks tighter approximations.
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ABSTRACT: We consider in this paper the robustness of decisions based on probabilistic thresholds under noisy sensor readings. In particular, we consider the stability of these decisions under different assumptions about the causal mechanisms that govern the output of a sensor. To this effect, we propose the same-decision probability as a query that can be used as a confidence measure for threshold-based decisions, and study some of its properties.
