R. Qi N. L. Zhang and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, pages 83--158, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....function: G = DF . The rest of the CPTs are positive. The moral graph is given in Figure 1b. Bucket elimination. Bucket elimination is a unifying algorithmic framework for variable elimination algorithms applicable to probabilistic and deterministic reasoning [Bertele and Brioschi, 1972, N. L. Zhang and Poole, 1994, Dechter, 1996] The input to a bucket elimination algorithm is a set of functions or relations. Given a variable ordering, the algorithm partitions the functions (e.g. CPTs) into buckets, where a function is placed in the bucket of its latest argument in the ordering. The algorithm processes ....

....with hidden variables Consider now the alternative of modeling clauses as CPTs. It requires expressing each clause as a CPT with a new hidden variable and the addition of evidence to the hidden nodes. Subsequently we can apply a regular variable elimination algorithm ( Dechter, 1996, N. L. Zhang and Poole, 1994] We call the resulting algorithm Elim Hidden. There is no substantial difference between Elim CPE and Elim Hidden in terms of worst case complexity. Processing the hidden variables creates tables that corresponds to the clauses which are placed in the same buckets that the original clauses ....

R. Qi N. L. Zhang and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, pages 83--158, 1994.

.... is a unifying algorithmic framework for variable elim D G A B C F A B C F G D Figure 1: Belief network P (g; f; d; c; b; a) P (gjf; d)P (f jc; b)P (djb; a)P (bja)P (cja)P (a) ination algorithms applicable to probabilistic and deterministic reasoning [Bertele and Brioschi, 1972, N. L. Zhang and Poole, 1994, Dechter, 1996] The input to a bucket elimination algorithm is a set of functions or relations. Given a variable ordering, the algorithm partitions the functions (e.g. CPTs) into buckets, where a function is placed in the bucket of its latest argument in the ordering. The algorithm processes ....

....with hidden variables Consider now the alternative of modeling clauses as CPTs. It requires expressing each clause as a CPT with a new hidden variable and the addition of evidence to the hidden nodes. Subsequently we can apply a regular variable elimination algorithm ( Dechter, 1996, N. L. Zhang and Poole, 1994] We call the resulting algorithm Elim Hidden. For completeness sake Algorithm Elim CPE Hidden in Figure 5 explicitly describes this approach. There is no substantial difference between Elim CPE and Elim Hidden in terms of worst case complexity. Processing the hidden variables creates tables ....

R. Qi N. L. Zhang and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, pages 83--158, 1994.

....standard assumption in an influence diagram of no forgetting , i.e. that values of observed variables and decisions that have been taken are remembered at all later times. We denote these more general diagrams by LIMIDs (LImited Memory Influence Diagrams) Such diagrams have also been studied by Zhang et al. 1994) with a similar motivation as ours under the name of decision networks. We have chosen to use a less general term. Partially observed Markov decision processes, also known as POMDPs, can be seen as special types of influence diagrams that develop over time. As opposed to fully observed Markov ....

....this strategy by message passing in a suitable junction tree. In Section 4 we establish general conditions for local optimal strategies to be globally optimal and provide algorithms for identifying such cases and reducing computational complexity. These results extend and generalize those of Zhang et al. 1994). 2 Describing LIMIDs 2.1 Diagrams LIMIDs are represented by directed acyclic graphs (DAGs) with three types of nodes. Chance nodes, displayed as circles, represent random variables. Decision nodes, displayed as squares, correspond to alternative choices available to the decision maker. Finally ....

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Zhang, N. L., Qi, R., and Poole, D. (1994). A computational theory of decision networks. International Journal of Approximate Reasoning, 11, 83--158.

.... i ; ejx Delta pa i )u(x Delta ) 1) where x Delta denotes an assignment x = x 1 ; xn ; d 1 ; d m ) where each d i is determined by ffi i 2 Delta as a functions of (x 1 ; xn ) Example 1 Figure 1 describes the influence diagram of the oil wildcatter problem (adapted from [ 8 ] The diagram shows that the test decision (T ) is to be made based on no information, and the drill (D) decision is to be made based on the decision to test (T) and the test results (R) The test results are dependent on test and seismic structure (S) which depends on an unobservable ....

....decision nodes. The rationale behind the no forgetting constraint is that information available now should be available later if the decision maker does not forget. In this paper, however we do not force these requirements. For a discussion of the implications of removing these restrictions see [ 8 ] Definition 1 (elimination functions) Given a function h defined over subset of variables S, where X 2 S, the functions ( P X h) is defined over U = S Gamma fXg as follows. For every U = u, P X h) u) P x h(u; x) Given a set of functions h 1 ; h j defined over the subsets S ....

R. Qi N. L. Zhang and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, pages 83--158, 1994.

....) 1) where x Delta denotes an assignment x = x 1 ; xn ; d 1 ; d m ) where each d i is determined by ffi i 2 Delta as a functions of (x 1 ; xn ) Namely: d i = ffi i (x) Example 1 Figure 1 describes the influence diagram of the oil wildcatter problem (adapted from (N. L. Zhang Poole 1994)) The diagram shows that the test decision (T ) is to be made based on no information, and the drill (D) decision is to be made based on the decision to test (T) and the test results (R) The test results are dependent on test and seismic structure (S) which depends on an unobservable variable ....

....nodes. The rationale behind the noforgetting constraint is that information available now should be available later if the decision maker does not forget. In this paper, however we do not force these requirements. For a discussion of the implications of removing these restrictions see (N. L. Zhang Poole 1994). Definition 1 (elimination functions) Given a function h defined over subset of variables S, where X 2 S, the functions ( P X h) is defined over U = S Gamma fXg as follows. For every U = u, P X h) u) P x h(u; x) Given a set of functions h 1 ; h j defined over the subsets S 1 ; ....

N. L. Zhang, R. Q., and Poole, D. 1994. A computational theory of decision networks. International Journal of Approximate Reasoning 83--158.

....in which they occur. This is referred to as coalescence. Bielza and Shenoy 6 [1981] Olmsted [1983] and Shachter [1986] Modifications of the symmetric ID solution technique have been proposed by Smith [1989] Shachter and Peot [1992] Ndilikilikesha [1994] Jensen et al. 1994] Cowell [1994] Zhang et al. 1994], Goutis [1995] and others. Besides SHM, asymmetric extensions of the influence diagram technique have been proposed by, e.g. Call and Miller [1990] Fung and Shachter [1990] and Qi et al. 1994] 3.1 ID Representation An influence diagram representation of a problem is specified at three ....

Zhang, N. L., R. Qi and D. Poole (1994), "A computational theory of decision networks," International Journal of Approximate Reasoning, 11(2), 83--158.

....or offer too much freedom, lacking the features of an appropriate knowledge representation formalism. In recent years, some research has been devoted to developing extensions to the representations discussed above, either to enhance their expressiveness as a knowledgerepresentation formalism (e.g. [12]) or to improve the computational efficiency of their evaluation (e.g. 3, 5] Being the most general representation method, Markov decision processes are becoming increasingly popular in AI as a basis for decisiontheoretic planning. For instance, Boutilier and colleagues [1] have developed an ....

N. L. Zhang, R. Qi, and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, 11(2):83--158, 1994.

No context found.

L. Zhang, Runping Qi and D. Poole (1993c), A computational theory of decision networks, accepted for publication on International Journal of Approximate Reasoning.

.... even the propositional, single agent without perfect recall case is exponentially harder to solve than an influence diagram [25] Intuitively this is because dynamic programming doesn t work when we have a forgetful agent; we can t solve the last decision independently of the earlier decisions [54] . This isn t a problem with the representation; it s the problems that are difficult. It isn t clear whether the representation in this formalism makes the problems more difficult to solve. There is some, however, evidence that the representation presented here makes solving a decision problem ....

L. Zhang, R. Qi, and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, 11(2):83--158, 1994.

....from the acyclicity of the logic program [Apt and Bezem, 1991] Definition 2.5 If is a set of sets, the expansion of , written 2628 4 is the set c 3 r X is a selector function on h . This constraint can be weakened slightly when the utility can be decomposed into sums [Zhang et al. 1994] 7 2 6 7 2 7h fLD . t L such that L dt . Otherwise the ICL DT theory is observation consistent. An ICL DT theory is observation complete if for all possible worlds , and for all )D , there exists ) such that qL . The above definitions are to make sure that we ....

....considered in this paper is how the representation can be exploited for computational gain. Influence diagram evaluation procedures can be divided into two classes: 1. Those that do dynamic programming, optimizing the last action first [Shachter, 1986; Cooper, 1988; Shachter and Peot, 1992; Zhang et al. 1994] 2. Those that convert the influence diagram into a decision tree (e.g. Howard and Matheson, 1981; Qi and Poole, 1995] and search it using a search method such as minimax [Ballard, 1983] Once it has been realised that efficient Bayesian network algorithms can be used for the ....

[Article contains additional citation context not shown here]

N. L. Zhang, R. Qi, and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, 11(2):83-- 158, 1994.

.... even the propositional, single agent without perfect recall case is exponentially harder to solve than an influence diagram [25] Intuitively this is because dynamic programming doesn t work when we have a forgetful agent; we can t solve the last decision independently of the earlier decisions [54] . This isn t a problem with the representation; it s the problems that are difficult. It isn t clear whether the representation in this formalism makes the problems more difficult to solve. There is some, however, evidence that the representation presented here makes solving a decision problem ....

L. Zhang, R. Qi, and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, 11(2):83--158, 1994.

No context found.

Zhang, L., R. Qi and D. Poole. 1993a. A computational theory of decision networks. accepted by International Journal of Approximate Reasoning, also available as a technical report 93-6, Department of Computer Science, UBC.

....model follows from the acyclicity of the logic program [Apt and Bezem, 1991] Definition 2.5 If S is a set of sets, the expansion of S, written expansion(S) is the set fR( j is a selector function on Sg. 2 This constraint can be weakened slightly when the utility can be decomposed into sums [Zhang et al. 1994] In Proceedings of the Eleventh Annual Conference on Uncertainty in Artificial Intelligence, Montreal, Quebec, Canada, August 18 20, 1995 The expansion of S corresponds to the cross product of the elements of S and, whenS consists of non intersecting sets, to the set of minimal hitting sets ....

....considered in this paper is how the representation can be exploited for computational gain. Influence diagram evaluation procedures can be divided into two classes: 1. Those that do dynamic programming, optimizing the last action first [Shachter, 1986; Cooper, 1988; Shachter and Peot, 1992; Zhang et al. 1994] 2. Those that convert the influence diagram into a decision tree (e.g. Howard and Matheson, 1981; Qi and Poole, 1995] and search it using a search method such as minimax [Ballard, 1983] Once it has been realised that efficient Bayesian network algorithms can be used for the ....

[Article contains additional citation context not shown here]

N. L. Zhang, R. Qi, and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, 11(2):83-- 158, 1994.

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R. Qi N. L. Zhang and D. Poole. A computational theory of decision networks. International Journal of Approximate Reasoning, pages 83--158, 1994.

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N. L. Zhang, R. Q., and Poole, D. 1994. A computational theory of decision networks. International Journal of Approximate Reasoning 83--158.

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-30. Zhang, N. L., Qi, R., and Poole, D. (1994). A computational theory of decision networks. International Journal of Approximate Reasoning, 11,

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