Judea Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241--288, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....variables may contain a certain degree of dependence and as a result the validity of a network can be questioned. Pearl proposed a star structure methodology to overcome the dependency problem by introducing a hidden node when any two nodes have strong conditional dependency given a common parent [Pearl, 1986][Verma and Pearl, 1991] Pearl s idea was to simulate the common cause between two nodes by introducing a hidden node, though he did not provide a mechanism for determining the parameters of a discrete node. Since a subjective approach to introduce a hidden node may not be effective due to lack of ....

....network. The NCIMI framework identifies as a principal feature of a Bayesian network the conditional independencies implied by the structure of the network, which are identified either by using the definition of the Bayesian network [Neapolitan, 1990] or by visual inspection employing dseparation [Pearl, 1986]. The conditional independencies implied by the structure of the network reflect the conditional independencies of the distribution represented by the network, and provide information about the network accuracy. According to the NCIMI framework, and in particular the NCI Theorem, a Bayesian ....

Pearl, J. Fusion, propagation, and structuring in belief networks. Artificial Intelligence. 29: 241-288, 1986.

....and Matheson (1981) Olmsted (1983) and Shachter (1988) developed an algorithm that reverses arcs in the network structure until the answer to the given probabilistic query can be read directly from the graph. In this algorithm, each arc reversal corresponds to an application of Bayes theorem. Pearl (1986) developed a message passing scheme that updates the probability distributions for eachnodeinaBayesian network in response to observations of one or more variables. Lauritzen and Spiegelhalter (1988) Jensen et al. 1990) and Dawid (1992) created an algorithm that first transforms the Bayesian ....

Pearl, J. (1986). Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241--288.

....of symptoms in our theory, are not so succinctly described. Finally, TNT allows for roles to act as evidence for or against other roles. This would result in a multiply connected network topology, which requires more complex methods for inference, such as clustering [47] cutset conditioning [24,26,36], or stochastic simulation [23] 9. Conclusion We have presented Topological iNference of Teleology (TNT) a theory of reasoning from structure to function in the domain of thermodynamic cycles. This theory describes a knowledge representation that enables efficient evidential reasoning from ....

J. Pearl, Fusion, propagation, and structuring in belief networks, Artificial Intelligence 29 (1986) 241--288.

....and Matheson (1981) Olmsted (1983) and Shachter (1988) developed an algorithm that reverses arcs in the network structure until the answer to the given probabilistic query can be read directly from the graph. In this algorithm, each arc reversal corresponds to an application of Bayes theorem. Pearl (1986) developed a message passing scheme that updates the probability distributions for each node in a Bayesian network in response to observations of one or more variables. Lauritzen and Spiegelhalter (1988) Jensen et al. 1990) and Dawid (1992) created an al gorithm that first transforms the ....

Pearl, J. (1986). Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241-288.

....rep resentation of the relationships between variables. It is a difficult task, however, to recognize these dependencies during the knowledge engineering of a network. It is especially difficult to distinguish nodes which are direct neighbors from those who are indirect neighbors. Pearl [15, 16, 17, 18, 19] has put forth a method for recovering this structure from a given probability distribution. This method has two parts. In the first part, all of the links of the network, without directionality, are discovered using an algorithm first put forth by Chow and Liu [4] As stated in Theorem 1, this ....

....database. Statistics were taken on how often the correct diagnosis was ranked first, second, etc. This should be a good indica tor of how well the network will perform when tested with other, more complicated methods such as those of belief revision and belief propagation as discussed in Pearl [15, 16, 17]. 4.4 Test Results The results of this testing, though not incredibly impressive, were quite promising. The results collected from testing the network on a test set of data are shown in Table 4.4. Although the network ranked the correct diagnosis first only 32 of the time, the correct diagnosis ....

Judea Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, September 1986.

....expert systems were purely rule based. Initial attempts to use probability theory in expert systems [4] hit a roadblock of limited computational power and the idea (and its unmanageable calculations) was abandoned for over 10 years. In 1986, Pearl introduced Bayesian networks to expert systems [10] and in 1989 Andreassen et al. [1] created MUNIN, a real world expert system which could perform disease diagnoses. MUNIN was the first example of Bayesian networks in an expert system. There are two early applications of Bayesian networks to gene expression data. Friedman et al. (2000) 3] the ....

J. Pearl, Fusion, propagation, and structuring in belief networks, Artificial Intelligence 29 (1986), no. 3, 241--288.

....proved that even the more general problem of nding approximate solutions belongs to the class of NP hard problems. Fundamentally, the problem of the propagation of evidence has been tackled in two di erent ways: With exact (or deterministic) algorithms. Most noticeable are the methods of Pearl [35], Shachter [42] and Lauritzen and Spiegelhalter [30] Jensen [23] improved aspects of the algorithm which was proposed in [30] With approximate algorithms, based on a simulation of the corresponding Bayesian network. We mention the algorithms introduced by Chavez and Cooper [3] Dagum and ....

....the DAG. 2. Triangulation of the resulting moral graph. The cliques of the triangulation de ne a decomposition of the Bayesian network. 3. Creation of the junction graph. 4. Creation of the junction tree. 5. Application, of a modi cation, of the evidence propagation algorithm for trees (Pearl [35]) to the junction tree. As can be read in Jensen [22, p. 67] The only problematic step in the process from DAG to junction tree is the triangulation. Since any elimination sequence will produce a triangulation it may not seem as a problem, but for the propagation algorithm it is. In ....

J. Pearl, Fusion, propagation, and structuring in belief networks, Artif. Intell. 29 (3) (1986) 241-288.

....nodes [126, 82, 97, 21, 116, 89] These express probabilistic relationships among states of the world exclusively, without explicit consideration of decisions and values. Several different terms are used for these representations, including causal networks, Bayesian nets, and belief networks [114]. We use belief networks, as this term is the most popular. Three Levels of Representation The expressiveness and sufficiency of influence diagrams is based in the representation s three levels of specification: relation, function, and number [82] We can express relations at one level without ....

....H n . We mentioned earlier that there has been recent work on the use of functions that specify patterns of independence. Recently, investigators have suggested methods for streamlining the probability assessment task, by specifying such prototypical functions for the probability distributions [56, 64, 114]. One example of a prototypical independence structure is termed the noisy OR gate. We review this structure as an example of the assessment savings that may be gained through identifying and representing analogous patterns of independence. The noisy OR structure is a probabilistic generalization ....

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J. Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241--288, 1986.

....Finally, Section 5 contains some conclusions and perspectives. It was not until recently, through discussions with A. P. Dempster, that we became aware that the work reported in this paper is in fact closely related to the Dempster Shafer theory of belief functions [7, 8, 32] and belief networks [33, 25, 26, 21] in statistics and artificial intelligence. Although our work has independent origins, several aspects are common with belief network theories. First, like the Dempster Shafer model of belief functions, the mixed systems we consider are not fully probabilized, and combine both random and unknown ....

....with constraint analysis. The composition we employ for building complex systems from simpler ones takes a form analog to Dempster s product intersection rule [8] for combining belief functions. Also, our incremental simulation scheme is similar in nature to the fusion propagation mechanism of [25, 26]. However, there exists an important difference between the partly directed, partly undirected graphs that we use to compile the dependency relations existing between the variables of a compound system, and the standard viewpoint of artificial intelligence, where directed branches encode ....

[Article contains additional citation context not shown here]

J. Pearl, Fusion, propagation, and structuring in belief networks, Artificial Intelligence, 29 (1986), pp. 241--288.

....expert depiction of corners. By joining each corner with its successor using straight lines, we obtain a polygonal approximation to the region which best ts expert annotation. This is used as evidence for buildings, as described in the following section. 2. 2 The Network Model Bayesian Networks [30, 31, 26] are directed acyclic graphs in which the nodes represent multivalued variables, comprising a collection of mutually exclusive and exhaustive hypotheses. The arcs signify direct dependencies between the linked variables and the strengths of these dependencies are quanti ed by conditional ....

J. Pearl. Fusion, propagation, and structuring in Belief Networks. Articial Intelligence, 29:241-288, 1986. 18

....for local refinement of an existent network. The feasibility of our approach is demonstrated by experiments involving networks of a practical size. Appears in Proceedings of Uncertainty in Artificial Intelligence 1993 Pages 243 250. 1 Introduction Bayesian networks, advanced by Pearl [Pea86], have become an important paradigm for representing and reasoning under uncertainty. Systems based on Bayesian networks have been constructed in a number of different application areas, ranging from medical diagnosis [BBS91] to oil price reasoning [Abr91] Despite these successes, a major ....

J. Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241--288, 1986.

....only the variable node l in common. Equation (6) for the soft output of the optimal decoder can now be written as C m = em Y i2I1 h 1 h i i Y i2I2 h 1 h i i Y i2I1 h 1 h i i Y i2I2 h 1 h i i : 7) The following theorem establishes the result of Pearl [5] that the belief propagation is optimal when the Tanner graph of the code is a tree. Theorem 3 Let variable node m belong to the Tanner graph of C 0 1 , and C1 m = m Y i2I1 1 h il l n 1 Y j 1 =0 j 1 6=l h ij 1 j 1 Y i2I 1 1 h il l n 1 Y j 1 =0 j 1 ....

J. Pearl, \Fusion, propagation, and structuring in belief networks," Articial Intelligence, Vol. 29, pp. 241-288, 1986. 10

....EM algorithm is often used to find the best parameters (Heckerman, 1995) Sometimes, hidden nodes (unobservable nodes) are introduced for several reasons. They are used for semantic reason, compactness of the structure (Binder et al. 1997) or to satisfy the axioms of conditional independence (Pearl, 1986). Since the CPT values of hidden nodes cannot be observed directly, several approaches have been proposed to obtain them (Pearl, 1986; Kwoh Gillies, 1996; Binder et al. 1997) Binder et al. 1997) introduced a gradient based approach, which can be applied generally. In this approach, the ....

....for several reasons. They are used for semantic reason, compactness of the structure (Binder et al. 1997) or to satisfy the axioms of conditional independence (Pearl, 1986) Since the CPT values of hidden nodes cannot be observed directly, several approaches have been proposed to obtain them (Pearl, 1986; Kwoh Gillies, 1996; Binder et al. 1997) Binder et al. 1997) introduced a gradient based approach, which can be applied generally. In this approach, the probability of observed evidence is maximized. In each iteration (or epoch) a conditional probability of a node and its parents is ....

Pearl, J. (1986). Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29, 241-288.

....distribution. Since the same data are used to update the importance function and to compute the estimator, this process introduces bias in the estimator. Heuristic importance rst removes edges from the network until it becomes a polytree, and then uses a modi ed version of the polytree algorithm (Pearl, 1986) to compute the likelihood functions for each of the unobserved nodes. Pr 0 (XnE) is a combination of these likelihood functions with Pr(XnE; e) In Step 7 heuristic importance does not update Pr k (XnE) As Shachter and Peot (1989) point out, this heuristic importance function can still lead ....

Pearl, J. (1986). Fusion, propagation, and structuring in belief networks. Articial Intelligence, 29 (3), 241-288.

....and (sets of) manifestations. A solution to a probabilistic abduction problem is a set A H such that the a posteriori probability P (AjM) is maximized. Several refinements and variants of probabilistic abduction have been introduced. Among the most important are Pearl s Belief Networks [56, 57] and Peng and Reggia s Probabilistic Causal Model [59] Probabilistic models are best used when the following three conditions are satisfied: 1. The structural relations between hypotheses and manifestations are rather simple; 2. the necessary probabilistic knowledge is available; and 3. ....

....is an irredundant preference (in fact, even partial) order based on a plausibility relation. The underlying assumptions of Bylander s work allows one to model certain parts of propositional logic [4] and is thus somewhat related to our work (see below) In the context of Bayesian belief networks [56], Cooper showed the intractability of calculating the probability that a certain hypothesis is present in some explanation, ignoring other hypotheses [16] For the logical approach, a number of very interesting complexity results for abduction on Horn theories have been derived by Selman and ....

J. Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241--288, 1986.

....information and the factorization formula depends on the type of the conditional independence graph. ABDUCTIVE INFERENCE WITH PROBABILISTIC NETWORKS 25 Bayesian networks. The most popular kind of probabilistic networks in artificial intelligence is the Bayesian network, also called belief network [Pearl, 1986; Pearl, 1992] A Bayesian network consists of a directed acyclic graph and a set of conditional probability distributions P ( A j parents(A) A 2 V , where parents(A) is the set of attributes corresponding to the parents of the node that corresponds to attribute A. That is, there is one ....

J. Pearl. Fusion, Propagation, and Structuring in Belief Networks. Artificial Intelligence 29:241--288, 1986.

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Judea Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241--288, 1986.

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J. Pearl. 1986. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29(3):241--288.

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J. Pearl, Fusion, propagation, and structuring in belief networks, Artificial Intelligence 29 (3) (1986) 241--288.

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J. Pearl, Fusion, propagation, and structuring in belief networks, Artificial Intelligence, 29: 241-288, 1986.

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J. Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241--288, 1986.

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Judea Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29(3):241--288, September 1986.

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J. Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241--248, 1986.

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J. Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29(3):24--288, 1986.

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Pearl, J., 1986, Fusion, propagation, and structuring in Belief Networks. Articial Intelligence, 29, 241-288.

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