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## Efficient Reasoning in Qualitative Probabilistic Networks (1993)

Venue: | In Proceedings of the 11th National Conference on Artificial Intelligence (AAAI--93 |

Citations: | 68 - 9 self |

### Citations

8903 |
Probabilistic reasoning in intelligent systems: networks of plausible inference
- Pearl
- 1988
(Show Context)
Citation Context ...hs, encounters the problem of a possibly infinite sequence of local belief propagation and an unstable equilibrium that does not necessarily correspond to the new probabilistic state of the network [ =-=Pearl, 1988-=-, pages 195--223 ] . Algorithms adapting the belief propagation paradigm to multiply connected belief networks treat loops in the underlying graph separately and essentially reduce the graph to a sing... |

696 | Good News and Bad News: Representation Theorems and Applications
- Milgrom
- 1981
(Show Context)
Citation Context ... that a qualitative influence between any two nodes in a network is also symmetric. Theorem 3 (symmetry) S ffi (a; b) implies S ffi (b; a). The theorem follows from the monotone likelihood property [ =-=Milgrom, 1981-=- ] . It shows merely that the sign of influence is symmetric. The magnitude of the influence of a variable a on a variable b can be arbitrarily different from the magnitude of the influence of b on a.... |

153 | Fundamental concepts of qualitative probabilistic networks.
- Wellman
- 1990
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Citation Context ...any kind of reasoning, one prefers stronger conclusions to weaker ones and this is captured by the canonical order of signs: 0 0 is preferred to 0 + and 0 \Gamma, and all three are preferred to 0 ? [ =-=Wellman, 1990-=-b ] . Qualitative properties can be elicited directly from a domain expert along with the graphical network using their common-sense interpretation or, alternatively, extracted from the numerical spec... |

110 |
Formulation of Trade-Offs in Planning under Uncertainty.
- Wellman
- 1990
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Citation Context ...01 henrion@camis.stanford.edu Abstract Qualitative Probabilistic Networks (QPNs) are an abstraction of Bayesian belief networks replacing numerical relations by qualitative influences and synergies [ =-=Wellman, 1990-=-b ] . To reason in a QPN is to find the effect of new evidence on each node in terms of the sign of the change in belief (increase or decrease). We introduce a polynomial time algorithm for reasoning ... |

93 |
A computational model for causal and diagnostic reasoning in inference engines.
- Kim, Pearl
- 1983
(Show Context)
Citation Context ... it. In previous work [ Henrion and Druzdzel, 1991 ] we introduced an approach called qualitative belief propagation, analogous to message-passing algorithms for quantitative belief networks (e.g., [ =-=Kim and Pearl, 1983-=- ] ), which traces the effect of an observation e on successive variables through a belief network to the targetst. Every node on the path from e to t is given a label that characterizes the sign of i... |

53 |
Qualitative propagation and scenario-based approaches to explanation in probabilistic reasoning
- Henrion, Druzdzel
- 1991
(Show Context)
Citation Context ...vailable or not necessary for the questions of interest. QPNs have been found valuable for such tasks as planning under uncertainty [ Wellman, 1990b ] and for explanation of probabilistic reasoning [ =-=Henrion and Druzdzel, 1991-=- ] . Like other qualitative schemes, QPNs are weaker than their quantitative counterparts, but they can provide more robust results with much less effort. QPNs are in essence a qualitative abstraction... |

52 | d-separation: From theorems to algorithms.
- Geiger, Verma, et al.
- 1990
(Show Context)
Citation Context ...fluence of a variable a on a variable b can be arbitrarily different from the magnitude of the influence of b on a. Of the definitions below, trail, head-to-head node, and active trail are based on [ =-=Geiger et al., 1990-=- ] . Definition 5 (trail in undirected graph) A trail in an undirected graph is an alternating sequence of nodes and links of the graph such that every link joins the nodes immediately preceding it an... |

31 | Intercausal reasoning with uninstantiated ancestor nodes
- Druzdzel, Henrion
- 1993
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Citation Context ...trary belief networks, we extended the definition of product synergy to accommodate this case. We reproduce here only the most important results. The complete derivations and proofs are reported in [ =-=Druzdzel and Henrion, 1993-=- ] . Definition 3 (half positive semi-definiteness) A square n \Theta n matrix M is called half positive semidefinite (half negative semi-definite) if for any nonnegative vector x consisting of n elem... |

31 | Probabilistic Reasoning in Decision Support Systems: From Computation to Common Sense.
- Druzdzel
- 1992
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Citation Context ...that are located on active trails from e to n. This requires a small amount of preprocessing, consisting of removal of irrelevant barren and ancestor nodes. The methods to do that are summarized in [ =-=Druzdzel, 1993-=- ] . m m m m m m \Delta \Delta \Delta \Delta \Deltaff A A A A AU H H Hj \Theta \Theta \Thetafl J J J \Omega \Omega \Omega\Gamma HeOx Temp Probe HeOx Temp Ox Tank Leak High Ox Temp Ox Pressure Probe He... |

15 | A decision-theoretic approach to the display of information for time-critical decisions: The Vista project
- Horvitz, Ruokangas, et al.
- 1992
(Show Context)
Citation Context ...0 ). Figure 1 shows an example of a QPN. This network is a small fragment of a larger belief network proposed for modeling an Orbital Maneuvering System (OMS) propulsion engine of the Space Shuttle [ =-=Horvitz et al., 1992-=- ] . The OMS engine's fragment captured by the m m m m m m \Delta \Delta \Delta \Delta \Deltaff A A A A AU H H Hj \Theta \Theta J J J J \Omega \Omega \Omega \Omega\Gamma HeOx Temp Probe HeOx Temp Ox T... |

6 | Explaining "explaining away - Wellman, Henrion - 1993 |

3 |
Qualitative intercausal relations, or explaining "explaining away
- Wellman, Henrion
- 1991
(Show Context)
Citation Context ... network to the targetst. Every node on the path from e to t is given a label that characterizes the sign of impact. This was further developed, with particular emphasis on intercausal reasoning in [ =-=Wellman and Henrion, 1991-=- ] . This approach differs from the graph reduction-based approach [ Wellman, 1990b ] in that it preserves the original structure of the network. The graph-reduction scheme performs inference by succe... |