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## Counting belief propagation (2009)

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Venue: | In Proc. UAI-09 |

Citations: | 50 - 20 self |

### Citations

8746 |
Probabilistic Reasoning in Intelligent Systems
- Pearl
- 1988
(Show Context)
Citation Context ...et of n discrete-valued random variables and let xi represent the possible realizations of random variable Xi. Graphical models compactly represent a joint distribution over X as a product of factors =-=[12]-=-, i.e., P (X = x) = 1 ∏ Z k fk(xk) . (1) Here, each factor fk is a non-negative function of a subset of the variables xk, and Z is a normalization constant. As long as P (X = x) > 0 for all joint conf... |

798 | Markov logic networks
- Richardson, Domingos
(Show Context)
Citation Context ...ymmetries not reflected in the graphical structure, and hence not exploited by BP. One of the most prominent examples are first-order and relational probabilistic models such as Markov logic networks =-=[14]-=-. Besides relational probabilistic models, however, there are also traditional, i.e., propositional probabilistic models that often produce inference problems with a lot of symmetries. In this work, w... |

665 | Loopy Belief-propagation for Approximate Inference: An Empirical Study
- Murphy, Weiss, et al.
- 1999
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Citation Context ...does have cycles. Although this loopy belief propagation has no guarantees of convergence or of giving the correct result, in practice it often does, and can be much more efficient than other methods =-=[11]-=-. To define the BP algorithm, we first introduce messages between variable nodes and their neighboring factor nodes and vice versa. The message from a variable X to a factor f is µX→f (x) = ∏ µh→X(x) ... |

538 |
A model for reasoning about persistence and causation
- Dean, Kanazawa
- 1989
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Citation Context ...l models and model counting of Boolean formulas. 5 Dynamic Relational Domains Stochastic processes evolving over time are widespread. Traditionally, graphical models such as dynamic Bayesian networks =-=[5]-=- have been used to represent uncertain processes over time. DBNs represent the state of the world as a set of variables, and model the probabilistic dependencies of the variables within and between ti... |

332 |
Introduction to Statistical Relational Learning
- Getoor, Taskar
- 2007
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Citation Context ...lations, as opposed to just random variables, have a long history in artificial intelligence. Recently, significant progress has been made in combining them with a principled treatment of uncertainty =-=[6, 2]-=-. First-order probabilistic models essentially combine graphical models with elements of firstorder logic by defining template factors (such as Poole’s parfactors [13]) that apply to whole sets of obj... |

298 | Tractable inference in complex stochastic processes
- Boyen, Koller
- 1998
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Citation Context ...ndom variables easily become correlated over time by virtue of sharing common influences in the past. Classical approaches to perform approximate inference in DBNs are the Boyen-Koller (BK) algorithm =-=[1]-=- and Murphy and Weiss’s factored frontier (FF) algorithm [10]. Both approaches have been shown to be equivalent to one iteration of BP but on different graphs [10]. BK, however, involves exact inferen... |

186 |
First-Order Probabilistic Inference
- Poole
- 2003
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Citation Context ...al domains, in which variables easily become correlated over time by virtue of sharing common influences in the past, is unclear and its evaluation is an interesting future work. Others such as Poole =-=[13]-=-, Braz et al. [3, 4], and Milch et al. [9] have developed lifted versions of the variable elimination algorithm. They typically also employ a counting elimination operator that is equivalent to counti... |

111 | Lifted First-Order Belief Propagation
- Singla, Domingos
- 2008
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Citation Context ...ational models and to model counting of Boolean formulas. Finally, we conclude and outline future research directions. 2 Related Work The closest work to CBP is the recent work by Singla and Domingos =-=[17]-=-. Actually, an investigation of their approach was the seed that grew into our proposal we present in this paper. Singla and Domingos’s lifted first-order belief propagation (LFOBP) builds upon [7] an... |

71 | Lifted probabilistic inference with counting formulas
- Milch, Zettlemoyer, et al.
- 2008
(Show Context)
Citation Context ...e correlated over time by virtue of sharing common influences in the past, is unclear and its evaluation is an interesting future work. Others such as Poole [13], Braz et al. [3, 4], and Milch et al. =-=[9]-=- have developed lifted versions of the variable elimination algorithm. They typically also employ a counting elimination operator that is equivalent to counting indistinguishable random variables and ... |

67 | Combining component caching and clause learning for effective model counting
- Sang, Bacchus, et al.
- 2004
(Show Context)
Citation Context ...es the most balanced variable u, uniformly randomly set u to true or false, (3) simplifies F by performing any possible unit propagations, and (4) repeats the process. An exact counter such as CACHET =-=[15]-=- is called when the formula is sufficiently simplified. At thisFigure 4: Ratios CBPCOUNT/BPCOUNT between 0.0 and 1.0 of the cummulative sum of edges computed respectively messages sent. A ratio of 1.... |

63 | The factored frontier algorithm for approximate inference in DBNs
- Murphy, Weiss
- 2001
(Show Context)
Citation Context ...of sharing common influences in the past. Classical approaches to perform approximate inference in DBNs are the Boyen-Koller (BK) algorithm [1] and Murphy and Weiss’s factored frontier (FF) algorithm =-=[10]-=-. Both approaches have been shown to be equivalent to one iteration of BP but on different graphs [10]. BK, however, involves exact inference, which for probabilistic logic models is extremely complex... |

36 | Exploiting shared correlations in probabilistic databases
- Sen
(Show Context)
Citation Context ..., no nodes and no features are grouped together. In contrast, CBP can directly be applied to any factor graph over finite random variables. In this sense, CBP is a generalization of LFOBP. Sen et al. =-=[16]-=- recently presented another “clustered” inference approach based on bisimulation. Like CBP, which can also be viewed as running a bisimulation-like algorithm on the factor graph, Sen et al.’s approach... |

28 | MPE and partial inversion in lifted probabilistic variable elimination
- Braz, Amir, et al.
- 1996
(Show Context)
Citation Context ...ch variables easily become correlated over time by virtue of sharing common influences in the past, is unclear and its evaluation is an interesting future work. Others such as Poole [13], Braz et al. =-=[3, 4]-=-, and Milch et al. [9] have developed lifted versions of the variable elimination algorithm. They typically also employ a counting elimination operator that is equivalent to counting indistinguishable... |

20 | Leveraging belief propagation, backtrack search, and statistics for model counting
- Kroc, Sabharwal, et al.
- 2008
(Show Context)
Citation Context ...elief Propagation Our approach, called CBPCOUNT, is based on BPCOUNT for computing a probabilistic lower bound on the model count of a Boolean formula F , which was recently introduced by Kroc et al. =-=[8]-=-. The basic idea is to efficiently obtain a rough estimate of the “marginals” of propositional variables using belief propagation with damping. The marginal of variable u in a set of satisfying assign... |

11 |
Lifted First Order Probabilistic Inference
- Braz, Amir, et al.
- 2005
(Show Context)
Citation Context ...ch variables easily become correlated over time by virtue of sharing common influences in the past, is unclear and its evaluation is an interesting future work. Others such as Poole [13], Braz et al. =-=[3, 4]-=-, and Milch et al. [9] have developed lifted versions of the variable elimination algorithm. They typically also employ a counting elimination operator that is equivalent to counting indistinguishable... |

10 |
Template-based inference in symmetric relational Markov random fields
- Jaimovich, Meshi, et al.
- 2007
(Show Context)
Citation Context ...s [17]. Actually, an investigation of their approach was the seed that grew into our proposal we present in this paper. Singla and Domingos’s lifted first-order belief propagation (LFOBP) builds upon =-=[7]-=- and also groups random variables, i.e., nodes that send and receive identical messages. CBP, however, differs from LFOBP in two important counts. First, CBP is conceptually easier thanLFOBP. This is... |