D. Geiger, T. S. Verma, and J. Pearl. Identifying independence in bayesian networks. Networks, 20:507--534, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on the potential p(x t 1 x t ) we need not pass messages from the (unique) cluster containing x t 1 to any other clusters. This is because x t 1 is an unobserved (directed) leaf of the graphical model a barren node and therefore does not impact the marginal distributions of the other nodes [Geiger et al. 1990] . Another case arises in a common type of odometry model p(y x) Often we have the following type of situation: the state of the robot x consists of pose variables p (e.g. the coordinates of the robot and its heading) and some derivatives p (e.g. the translational and rotational ....

D. Geiger, T. S. Verma, and J. Pearl. Identifying independence in bayesian networks. Networks, 20:507--534, 1990. 42

....In the design and implementation of probabilistic reasoning or database systems, a crucial issue to consider is the implication problem. The implication problem has been extensively studied in both relational databases, including [2] 3] 24] 26] 27] and in Bayesian networks [13] [15], 30] 33] 36] 37] 41] 46] The implication problem is to test whether a given input set of independencies logically implies another independency . Traditionally, axiomatization was studied in an attempt to solve the implication problem for data and probabilistic conditional ....

D. Geiger, T. Verma, and J. Pearl, "Identifying independence in bayesian networks," Univ. California, Tech. Rep. R-116, 1988.

....an improvement of the algorithm suitable for belief updating only. The beliefupdating task has special semantics which allows restricting the computation to relevant portions of the belief network. These restrictions are already available in the literature in the context of the existing algorithms [27, 44]. Since summation over all values of a probability function is 1, the recorded functions of some buckets will degenerate to the constant 1. If we can predict these cases in advance, we can avoid needless computation by skipping some buckets. If we use a topological ordering of the belief ....

D. Geiger, T. Verma, and J. Pearl. Identifying independence in bayesian networks. Networks, 20:507--534, 1990.

.... exist two Bayesian networks B 1 and B 2 over G, that are identical except in the CPD they assign to Z, but PB1 (X j Y ) 6= PB2 (X j Y ) As we will see, the decision rule at D 0 is only relevant to D if D 0 (viewed as a chance node) is a requisite probability node for P (UD j D;Pa(D) Geiger et al. 1990] provide a graphical criterion for testing whether a node Z is a requisite probability node for a query P (X j Y ) We add to Z a new dummy parent b Z whose values correspond to CPDs for Z, selected from some set of possible CPDs. Then Z is a requisite probability node for P (X j Y ) if and only ....

D. Geiger, T. Verma, and J. Pearl. Identifying independence in Bayesian networks. Networks, 20:507--534, 1990.

....xed, would changing X alter Y Formal interest in this notion appears in the works of Suppes [8] and Salmon [7] who attempted to give it probabilistic interpretation. This paper pursues a logical approach, and starts with the work by Galles and Pearl [2] which, similar to the work on graphoids [5, 3], is based on a set of axioms and rules of inference that de nes a formal deductive system. In this system, causal relevance is expressed by logical formulas and new relevance sentences can be derived from old ones through rules of inference. Such deductive system requires an interpretation; that ....

D. Geiger, T. Verma and J. Pearl (1990). Identifying Independence in Bayesian Networks. Networks 20, pp. 507-534.

....to this function by y(x 1 ; xn ) or p(a j e) x 1 ; xn ) The subset of parameters of a network in uencing the posterior marginal is a function of the evidence, e. The set of in uential (or relevant) parameters can easily be identi ed using a variation of the algorithm described by Geiger et al. 1990), as described in the paper by Castillo et al. 1997) Having identi ed the set of, say n, relevant parameters, x 1 ; xn , the algorithm of Castillo et al. 1997) identi es the set of monomials for which the coecients will be non zero in the linear function p(a; e) x 1 ; xn ) If ....

Geiger, D., Verma, T. & Pearl, J. (1990). Identifying independence in Bayesian networks, Networks 20(5): 507-534. Special Issue on In uence Diagrams.

....) as indicated in Figure 1. The independence relations in the Markov condition imply several other independence relations among variables in a network. The complete relationship between probabilistic independence and the graphical structure of the network is given by the concept of d separation [5]. Definition 1 Given three sets of variables X, Y and Z, To appear, Workshop on Probabilistic Reasoning in Artificial Intelligence, Atibaia, Brazil, November 20, 2000 = Z Z Z Z Z Z = s= A B C D E F G Probability ....

....of p(X q jE) typically involves only a subset of the densities associated with the network. If density p(X i jpa(X i ) is necessary for answering a query, then X i is a requisite variable [12] There are polynomial algorithms to obtain requisite variables based on graph separation properties [5, 12]. Denote by XR the set of requisite variables. Variables in X q necessarily belong to XR , but not all observed variables belong to XR (only observed variables that have non observed parents in XR belong to XR ) We are interested in computing the following expression: p(X q ; E) X XRnfXq ....

D. Geiger, T. Verma, and J. Pearl. Identifying independence in Bayesian networks. Networks, 20:507-- 534, 1990.

....Example 1. The Markov and the contraction conditions lead to d separation properties for epistemic independence, when we require equivalence of credal sets for epistemic independence (De nition 1) In this case, the conditions allow a duplication of the d separation proof for Bayesian networks [13]. The contraction condition is necessary because epistemic independence does not satisfy precisely the graphoid property of contraction employed in Verma, Geiger and Pearl s proof of d separation [9] Note that the contraction condition is not satis ed in Example 1. Note also that if we require ....

D. Geiger, T. Verma, and J. Pearl. Identifying independence in Bayesian networks. Networks, 20:507-534, 1990.

....can be verified in time linear in the size of the graph (Geiger et al. 1989) Identification of requisite information can also be determined in time linear in the size of the graph. These algorithms have been generalized to deal with deterministic nodes in belief networks and influence diagrams (Geiger et al. 1990; Shachter 1990) This paper introduces the Bayes Ball algorithm, a simpler and more e#cient algorithm to identify conditional irrelevance and requisite information. For belief networks, Bayes Ball runs in time linear in the size of the active part of the graph, so it is considerably faster when ....

....irrelevance and requisite information. For belief networks, Bayes Ball runs in time linear in the size of the active part of the graph, so it is considerably faster when most of a graphical knowledge base is irrelevant. It also corrects an error in the requisite information algorithm given in Geiger (1990). More significantly, for decision problems it runs in time linear in the size of the graph; up until now the fastest algorithm (Shachter 1990) has been O( number of decisions) graph size) Finally, the decision algorithm has been extended to allow multiple separable value nodes. The ....

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Geiger, D., T. Verma, and J. Pearl. "Identifying independence in Bayesian networks." Networks 20 (1990): 507-534.

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D. Geiger, T.S. Verma, and J. Pearl. Identifying independence in Bayesian networks. Networks, 20(5):507--534, 1990.

....but if v is selected it does not break loops formed by traversing a path a v b, where both edges point into v. The theory is well developed in [26] and it is based on a graph theory criterion called d separation that fully characterizes which vertices are conditionally independent of others [11]. This criterion must justify any solution to the inference problem because any solution must use the properties of conditional independence in order to be efficient. For marriage graphs the selection of loop breakers is conceptually easier because marriage vertices cannot be selected and ....

Geiger D, Verma TS, Pearl J: Identifying independence in Bayesian networks. Networks 1990; 20:507--534.

....blocked by ft 1 ; t m g, then the corresponding sets of variables fu r1 ; u r l g and fu s1 ; u sk g are independent conditioned on fu t 1 ; u t m g. Furthermore, Geiger and Pearl [GP90] proved a converse to this theorem. Both results are presented and extended in [GVP90]. Using the close relationship between blocked trails and conditional independence, Kim and Pearl [KP83] developed an algorithm update tree that solves the updating problem on Bayesian networks in which every two vertices are connected with at most one trail. These networks are called ....

Geiger D., Verma T.S., and Pearl J., Identifying independence in Bayesian networks, Networks, 20 (1990), 507--534.

....the equation ae ij Deltam = ae ij Gamma ae im ae jm ) 1 Gamma ae 2 im ) 1 2 (1 Gamma ae 2 jm ) 1 2 which renders ae ij Deltam 6= 0 when ae ij = 0. The same applies to the partial correlation ae ij Deltam 0 where m 0 is any descendant of m. Theorem 1 [Verma and Pearl, 1988; Geiger et al. 1990] If sets X and Y are d separated by Z in a DAG G then X is independent of Y conditional on Z in every Markovian model structured according to G. Conversely, if X and Y are not d separated by Z in a DAG G, then X and Y are dependent conditional on Z in almost all Markovian models structured ....

D. Geiger, T.S. Verma, and J. Pearl. Identifying independence in Bayesian networks. In Networks, volume 20, pages 507--534. John Wiley, Sussex, England, 1990.

....blocked by ft 1 ; t m g, then the corresponding sets of variables fu r1 ; u r l g and fu s1 ; u sk g are independent conditioned on fu t 1 ; u t m g. Furthermore, Geiger and Pearl [GP90] proved a converse to this theorem. Both results are presented and extended in [GVP90]. Using the close relationship between blocked trails and conditional independence, Kim and Pearl [KP83] developed an algorithm update tree that solves the updating problem on Bayesian networks in which every two vertices are connected with at most one trail (singly connected) Pearl then solved ....

Geiger, D., Verma, T.S., and Pearl, J., Identifying independence in Bayesian networks, Networks, 20 (1990), 507--534.

....blocked by ft 1 ; t m g, then the corresponding sets of variables fu r1 ; u r l g and fu s1 ; u sk g are independent conditioned on fu t 1 ; u t m g. Furthermore, Geiger and Pearl proved a converse to this theorem [GP90] Both results are presented and extended in [GVP90]. Using the close relationship between blocked trails and conditional independence, Kim and Pearl [KP83] developed an algorithm update tree that solves the updating problem on Bayesian networks in which every two vertices are connected with at most one trail (singly connected) Pearl then solved ....

Geiger D., Verma T.S., and Pearl J., Identifying independence in Bayesian networks, Networks, 20 (1990), 507--534.

.... once the value of v is known, a and b become dependent and a virtual edge connects them) The theory explaining this constraint is developed in [6] and it is based on a graph theoretic criterion called d separation that fully characterizes which vertices are conditionally independent of others [18]. This criterion is used to justify any solution to the inference problem because any solution must use the properties of conditional independence in order to be efficient. For marriage graphs the selection of loop breakers is conceptually easier because marriage vertices cannot be selected and ....

Geiger D, Verma TS, Pearl J: Identifying independence in Bayesian networks. Networks 1990; 20:507--534.

....deterministic definition, causal irrelevance complies with all of the axioms of path interception in cyclic graphs, with the exception of transitivity. We compare our formalism to that of [Lewis, 1973] and offer a graphical method of proving theorems about causal relevance. 1 Introduction In [Geiger et al. 1990], a set of axioms was developed for a class of relations called graphoids. These axioms characterize informational relevance 1 among observed events based on the semantics of conditional independence in probability calculus. This paper develops a parallel set of axioms for causal relevance, that ....

....(at z) changing X will not affect the probability of Y . 3. 1 Comparison to Informational Relevance If we remove the hats from Definition 3 above, we get the standard definition of conditional independence in probability calculus, denoted I(X; Z; Y ) which is governed by the graphoid axioms [Geiger et al. 1990] given in Figure 3 1.1 (Symmetry) I(X; Z; Y ) I(Y; Z; X) 1.2 (Decomposition) I(X; Z; Y W ) I(X; Z; Y ) 1.3 (Weak union) I(X; Z; Y W ) I(X; ZW;Y ) 1.4 (Contraction) I(X; Z; Y ) I(X; ZY;W ) I(X; Z; Y W ) 1.5 (Intersection) I(X; ZY;W ) I(X; ZW;Y ) I(X; Z; Y W ) Intersection ....

D. Geiger, T.S. Verma, and J. Pearl. Identifying independence in Bayesian networks. In Networks, volume 20, pages 507--534. John Wiley and Sons, Sussex, England, 1990.

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D. Geiger, T. S. Verma, and J. Pearl. Identifying independence in bayesian networks. Networks, 20:507--534, 1990.

No context found.

D. Geiger, T. Verma, and J. Pearl. Identifying independence in Bayesian networks. Networks, 20:507-534, 1990.

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Dan Geiger, Thomas S. Verma, and Judea Pearl. Identifying independence in Bayesian networks. Networks, 20(5):507--534, August 1990.

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D. Geiger, T. Verma, and J. Pearl. Identifying independence in bayesian networks. Technical Report R-116, University of California, 1988.

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D. Geiger, T. S. Verma, and J. Pearl. Identifying independence in bayesian networks. Networks, 20:507--534, 1990. 42

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D. Geiger, T. Verma, J. Pearl. Identifying Independence in Bayesian Networks. Networks, 20:507-534, 1990.

No context found.

Dan Geiger, Thomas S. Verma, and Judea Pearl. Identifying independence in Bayesian networks. Networks, 20(5):507--534, August 1990.

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D. Geiger, T. Verma, and J. Pearl. Identifying independence in Bayesian Networks. Networks, 20:507--534, 1990.

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