## Exploiting Causal Independence in Bayesian Network Inference (1996)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 155 - 9 self |

### BibTeX

@ARTICLE{Zhang96exploitingcausal,

author = {Nevin Lianwen Zhang and David Poole},

title = {Exploiting Causal Independence in Bayesian Network Inference},

journal = {Journal of Artificial Intelligence Research},

year = {1996},

volume = {5},

pages = {301--328}

}

### Years of Citing Articles

### OpenURL

### Abstract

A new method is proposed for exploiting causal independencies in exact Bayesian network inference.

### Citations

7043 |
Probabilistic reasoning in intelligent systems: networks of plausible inference
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- 1988
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Citation Context ...ability theory. The probabilistic approach is now by far the most popular among all those alternatives, mainly due to a knowledge representation framework called Bayesian networks or belief networks (=-=Pearl, 1988-=-; Howard & Matheson, 1981). Bayesian networks are a graphical representation of (in)dependencies amongst random variables. A Bayesian network (BN) is a DAG with nodes representing random variables, an... |

1283 |
Local computations with probabilities on graphical structures and their application to expert systems
- Lauritzen, Spiegelhalter
- 1988
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Citation Context ..., the number of probabilities required can be much less than the number required if there were no independencies. The structure can be exploited computationally to make inference faster (Pearl, 1988; =-=Lauritzen & Spiegelhalter, 1988-=-; Jensen et al., 1990; Shafer & Shenoy, 1990). The definition of a Bayesian network does not constrain how a variable depends on its parents. Often, however, there is much structure in these probabili... |

580 |
The computational complexity of probabilistic inference using bayesian belief networks
- Cooper
- 1990
(Show Context)
Citation Context ...e computationof sum-out(F ; z 1 ), and those are often only a small portion of all the variables. This is why inference in a BN can be tractable in many cases, even if the general problem is NP-hard (=-=Cooper, 1990-=-). 3. The Variable Elimination Algorithm Based on the discussionsof the previous section, we present a simple algorithm for computingP (X jY =Y 0 ). The algorithm is based on the intuitions underlying... |

351 |
Influence diagrams
- Howard, Matheson
- 1981
(Show Context)
Citation Context ...y. The probabilistic approach is now by far the most popular among all those alternatives, mainly due to a knowledge representation framework called Bayesian networks or belief networks (Pearl, 1988; =-=Howard & Matheson, 1981-=-). Bayesian networks are a graphical representation of (in)dependencies amongst random variables. A Bayesian network (BN) is a DAG with nodes representing random variables, and arcs representing direc... |

324 |
Complexity of finding embeddings in a k-tree
- Arnborg, Corneil, et al.
- 1987
(Show Context)
Citation Context ...ltiplications and numerical summations it performs. An optimal elimination ordering is one that results in the least complexity. The problem of finding an optimal elimination ordering is NP-complete (=-=Arnborg et al., 1987-=-). Commonly used heuristics include minimum deficiency search (Bertelè & Brioschi, 1972) and maximum cardinality search (Tarjan & Yannakakis, 1984). Kjærulff (1990) has empirically shown that minimum ... |

294 | Probabilistic Horn abduction and Bayesian networks - Poole - 1993 |

288 | Context-specific independence in Bayesian networks - Boutilier, Friedman, et al. - 1996 |

288 | Bucket elimination: a unifying framework for probabilistic inference - Dechter - 1996 |

287 |
Bayesian Updating in Causal Probabilistic Networks by Local Computations
- Jensen, Lauritzen, et al.
- 1990
(Show Context)
Citation Context ...uired can be much less than the number required if there were no independencies. The structure can be exploited computationally to make inference faster (Pearl, 1988; Lauritzen & Spiegelhalter, 1988; =-=Jensen et al., 1990-=-; Shafer & Shenoy, 1990). The definition of a Bayesian network does not constrain how a variable depends on its parents. Often, however, there is much structure in these probabilityfunctions that can ... |

179 |
Nonserial Dynamic Programming
- Bertelè, Brioschi
- 1972
(Show Context)
Citation Context ... is one that results in the least complexity. The problem of finding an optimal elimination ordering is NP-complete (Arnborg et al., 1987). Commonly used heuristics include minimum deficiency search (=-=Bertelè & Brioschi, 1972-=-) and maximum cardinality search (Tarjan & Yannakakis, 1984). Kjærulff (1990) has empirically shown that minimum deficiency search is the best existing heuristic. We use minimum deficiency search in o... |

140 |
Independence properties of directed markov fields
- Lauritzen, Dawid, et al.
- 1990
(Show Context)
Citation Context ...e start of the algorithm), but each observation in CTP requires propagation of evidence. Because VE is query oriented, we can prune nodes that are irrelevant to specific queries (Geiger et al., 1990; =-=Lauritzen et al., 1990-=-; Baker & Boult, 1990). In CTP, on the other hand, the clique tree structure is kept static at run time, and hence does not allow pruning of irrelevant nodes. CTP encodes a particular space-time trade... |

111 |
Subjective Bayesian methods for rule-based inference systems
- Duda, Hart, et al.
- 1976
(Show Context)
Citation Context ...in larger networks than previous algorithms. 1. Introduction Reasoning with uncertain knowledge and beliefs has long been recognized as an important research issue in AI (Shortliffe & Buchanan, 1975; =-=Duda et al., 1976-=-). Several methodologies have been proposed, including certainty factors, fuzzy sets, Dempster-Shafer theory, and probability theory. The probabilistic approach is now by far the most popular among al... |

108 |
Some practical issues in constructing belief networks
- Henrion
- 1987
(Show Context)
Citation Context ...ndently to a common effect. A well-known example is the noisy OR-gate model (Good, 1961). Knowledge engineers have been using specific causal independence models in simplifying knowledge acquisition (=-=Henrion, 1987-=-; Olesen et al., 1989; Olesen & Andreassen, 1993). Heckerman (1993) was the first to formalize the general concept of causal independence. The formalization was later refined by Heckerman and Breese (... |

106 |
Probability propagation
- G, Shenoy
- 1990
(Show Context)
Citation Context ...s than the number required if there were no independencies. The structure can be exploited computationally to make inference faster (Pearl, 1988; Lauritzen & Spiegelhalter, 1988; Jensen et al., 1990; =-=Shafer & Shenoy, 1990-=-). The definition of a Bayesian network does not constrain how a variable depends on its parents. Often, however, there is much structure in these probabilityfunctions that can be exploited for knowle... |

99 | Knowledge engineering for large belief networks - Pradhan, Provan, et al. - 1994 |

97 |
A model of inexact reasoning in medicine
- Shortliffe, Buchanan
- 1975
(Show Context)
Citation Context ...s for inference in larger networks than previous algorithms. 1. Introduction Reasoning with uncertain knowledge and beliefs has long been recognized as an important research issue in AI (Shortliffe & =-=Buchanan, 1975-=-; Duda et al., 1976). Several methodologies have been proposed, including certainty factors, fuzzy sets, Dempster-Shafer theory, and probability theory. The probabilistic approach is now by far the mo... |

93 |
Knowledge representation and inference in similarity networks and bayesian multinets
- Geiger, Heckerman
- 1996
(Show Context)
Citation Context ... such dependencies can be stated as rules (Poole, 1993), trees (Boutilier c 1996 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved.ZHANG & POOLE et al., 1996) or as multinets (=-=Geiger & Heckerman, 1996-=-). Another is where the the function can be described using a binary operator that can be applied to values from each of the parent variables. It is the latter, known as ‘causal independencies’, that ... |

81 | A computational model for causal and diagnostic reasoning in inference systems - JH, Pearl - 1983 |

71 | A generalization of noisy-or model - Srinivas - 1993 |

70 | A new look at causal independence - HECKERMAN, BREESE - 1994 |

69 | Parameter adjustment in Bayes networks: The generalized noisy orgate
- Diez
- 1993
(Show Context)
Citation Context ...erent than that given by Heckerman and Breese (1994) and Srinivas (1993). However, it still covers common causal independence models such as noisy OR-gates (Good, 1961; Pearl, 1988), noisy MAX-gates (=-=Díez, 1993-=-), noisy AND-gates, and noisy adders (Dagum & Galper, 1993) as special cases. One can see this in the following examples. Example 1 (Lottery) Buying lotteries affects your wealth. The amounts of money... |

67 | Symbolic probabilistic inference in belief networks - Shachter, D’Ambrosio, et al. - 1990 |

53 |
Simple linear time algorithms to test chordiality of graphs, test acyclicity of graphs, and selectively reduce acyclic hypergraphs
- Tarjan, Yannakakis
- 1984
(Show Context)
Citation Context ...of finding an optimal elimination ordering is NP-complete (Arnborg et al., 1987). Commonly used heuristics include minimum deficiency search (Bertelè & Brioschi, 1972) and maximum cardinality search (=-=Tarjan & Yannakakis, 1984-=-). Kjærulff (1990) has empirically shown that minimum deficiency search is the best existing heuristic. We use minimum deficiency search in our experiments because we also found it to be better than t... |

43 | Causal independence for knowledge acquisition and inference
- Heckerman
- 1993
(Show Context)
Citation Context ...ich requires 2 2 numerical multiplications. 9. Previous Methods Two methods have been proposed previously for exploiting causal independence to speed up inference in general BNs (Olesen et al., 1989; =-=Heckerman, 1993-=-). They both use causal independence to transform the topology of a BN. After the transformation, conventional algorithms such as CTP or VE are used for inference. We shall illustrate those methods by... |

41 | Efficient inference in Bayes networks as a combinatorial optimization problem - Li, D’Ambrosio - 1994 |

40 | D-separation: from theorems to algorithms
- Geiger, Verma, et al.
- 1989
(Show Context)
Citation Context ... are eliminated at the start of the algorithm), but each observation in CTP requires propagation of evidence. Because VE is query oriented, we can prune nodes that are irrelevant to specific queries (=-=Geiger et al., 1990-=-; Lauritzen et al., 1990; Baker & Boult, 1990). In CTP, on the other hand, the clique tree structure is kept static at run time, and hence does not allow pruning of irrelevant nodes. CTP encodes a par... |

35 | Triangulation of Graphs: Algorithms Giving Small Total State Space - Kjærulff - 1990 |

34 |
A munin network for the median nerve - a case study in loops
- Olesen, Kjarulff, et al.
- 1989
(Show Context)
Citation Context ...mmon effect. A well-known example is the noisy OR-gate model (Good, 1961). Knowledge engineers have been using specific causal independence models in simplifying knowledge acquisition (Henrion, 1987; =-=Olesen et al., 1989-=-; Olesen & Andreassen, 1993). Heckerman (1993) was the first to formalize the general concept of causal independence. The formalization was later refined by Heckerman and Breese (1994). Kim and Pearl ... |

33 |
A causal calculus I
- Good
- 1961
(Show Context)
Citation Context ... that we seek to exploit in this paper. Causal independence refers to the situation where multiple causes contribute independently to a common effect. A well-known example is the noisy OR-gate model (=-=Good, 1961-=-). Knowledge engineers have been using specific causal independence models in simplifying knowledge acquisition (Henrion, 1987; Olesen et al., 1989; Olesen & Andreassen, 1993). Heckerman (1993) was th... |

30 | Local expression languages for probabilistic dependence - D’Ambrosio - 1991 |

20 |
Pruning Bayesian networks for efficient computation
- Baker, Boult
- 1990
(Show Context)
Citation Context ...), but each observation in CTP requires propagation of evidence. Because VE is query oriented, we can prune nodes that are irrelevant to specific queries (Geiger et al., 1990; Lauritzen et al., 1990; =-=Baker & Boult, 1990-=-). In CTP, on the other hand, the clique tree structure is kept static at run time, and hence does not allow pruning of irrelevant nodes. CTP encodes a particular space-time tradeoff, and VE another. ... |

18 | Using causal knowledge to create simulated patient cases: the CPCS project as an extension of INTERNIST-1 - Parker, Miller - 1987 |

15 | Symbolic probabilistic inference in large BN2O networks - D’Ambrosio - 1994 |

7 |
Additive belief network models
- Dagum, Galper
- 1993
(Show Context)
Citation Context ...994) and Srinivas (1993). However, it still covers common causal independence models such as noisy OR-gates (Good, 1961; Pearl, 1988), noisy MAX-gates (Díez, 1993), noisy AND-gates, and noisy adders (=-=Dagum & Galper, 1993-=-) as special cases. One can see this in the following examples. Example 1 (Lottery) Buying lotteries affects your wealth. The amounts of money you spend on buying different kinds of lotteries affect y... |

7 |
Parameter adjustment in bayes networks. the generalized noisy or-gate
- Dez
- 1993
(Show Context)
Citation Context ...erent than that given by Heckerman and Breese (1994) and Srinivas (1993). However, it still covers common causal independence models such as noisy OR-gates (Good, 1961; Pearl, 1988), noisy MAX-gates (=-=Dez, 1993-=-), noisy AND-gates, and noisy adders (Dagum & Galper, 1993) as special cases. One can see this in the following examples. Example 1 (Lottery) Buying lotteries affects your wealth. The amounts of money... |

7 | Triangulation of graphs - algorithms giving small total state space - Kjrulff - 1990 |

5 |
Specification of models in large expert systems based on causal probabilistic networks
- Olesen, Andreassen
- 1993
(Show Context)
Citation Context ...nown example is the noisy OR-gate model (Good, 1961). Knowledge engineers have been using specific causal independence models in simplifying knowledge acquisition (Henrion, 1987; Olesen et al., 1989; =-=Olesen & Andreassen, 1993-=-). Heckerman (1993) was the first to formalize the general concept of causal independence. The formalization was later refined by Heckerman and Breese (1994). Kim and Pearl (1983) showed how the use o... |

1 |
The computational complexity of probabilisticinference using Bayesian belief networks
- Cooper
- 1990
(Show Context)
Citation Context ...n the computationofsum-out(F;z 1), and those are often only a small portion of all the variables. This is why inference in a BN can be tractable in many cases, even if the general problem is NP-hard (=-=Cooper, 1990).-=- 3. The Variable Elimination Algorithm Based on the discussionsof the previous section, we present a simple algorithmfor computingP(XjY =Y 0). The algorithm is based on the intuitions underlying D’A... |

1 | Additivebelief-network models - Dagum - 1993 |

1 | Knowledgerepresentation and inference in similarity networks and Bayesian multinets - Geiger - 1996 |

1 | ProbabilisticHorn abduction and Bayesian networks - Poole - 1993 |

1 | Probabilistic Horn abductionand Bayesian networks - Poole - 1993 |