Prakash P. Shenoy. 1991. Valuation-based systems for Bayesian decision analysis. Operations Research, 40:463--484.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....node is a real valued function with domain pa(U ) The domain rules for chance potentials are similar to the rules for belief graphs, and apart from the operations for belief potentials, there is an operation for combining chance potentials and belief potentials. This is treated in more detail by [17] under the term valuation networks. The term in uence diagram is reserved to valuation networks based on Bayesian networks, where the combination of probabilities and utilities is the usual expectation operation. Figure 7 gives an example of an in uence diagram. H B I E K J G C A U3 U2 ....

....of the past yields a state of D. A strategy for an in uence diagram is a set of policies, one for each decision variable. An optimal strategy is a strategy yielding maximal expected utility. We have algorithms well suited for calculating an optimal strategy for a speci ed in uence diagram ([17], 5] 14] The algorithms exploit dynamic programming by passing through the in uence diagram in reverse temporal order. For each decision, an optimal policy is determined and altogether these policies form an optimal strategy. The complexity of solving an in uence diagram is in general higher ....

Prakash P. Shenoy. Valuation-based systems for Bayesian decision analysis. Operations Research, 40(3):463-484, 1992.

....tree, a concept we discuss in more detail in subsequent sections. As we will see, MR processes possessing such a Markov property make contact with standard Markov processes in time, with Markov random fields (MRF s) and with the large class of Bayes nets, belief networks, and graphical models [204, 170, 267, 35, 36, 169, 108, 128, 339, 89, 294, 295, 143, 168, 123, 197, 236, 337, 357, 302]. It is the exploitation of this Markovian property that leads to the e#cient algorithms that we describe. 1.3 Getting oriented A fair question to ask is: for whom is this paper written A reply that is only partially frivolous is: for the author. The reason is not self promotion (although the ....

....p(x(0) at the root node and the parent child transition distributions p(x(s) x(s#) for every node s #=0. Such models have a long history, extending back to studies in statistical physics [26] dynamic programming [32] artificial intelligence and other investigations of graphical models [267, 294, 295, 89, 128, 7, 169], and signal and image processing [42, 80, 261, 199, 58, 59, 283, 175, 281, 213] Later in this paper we will illustrate examples of such models for two di#erent purposes. One is a class of image segmentation problems [42, 199, 58] as introduced in Section 2.5 in which the discrete variable at ....

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G.R. Shafer and P.P. Shenoy. Valuation-based systems for Bayesian decision analysis. Operations Research, 40:463--484, 1992.

....nodes; namely they both indicate dependence. It is evident that the no forgetting constraint is not compatible with the new interpretation of arcs into decision nodes. It needs to be lifted. 1.3.2. Lifting the single value node constraint As pointed out by Tatman and Shachter [38] and by Shenoy [35], the total utility of a decision problem can sometimes be decomposed into several components. In our extended oil wildcatter problem, for instance, utility can decomposed into the sum of four components, namely test cost, drill cost, sale cost, and oil sales. In such a case, we assign one value ....

....to smooth N at d, decompose N at d into a tail and a body, find an optimal decision function for d in the tail, and repeat the process for the body. An disadvantage of this approach is that TAIL SMOOTHING may demand many arc reversals, which are known to be a cause of inefficiency (Shenoy [35], Ndilikilikesha [19] The motivation behind EVALUATE1 is to avoid arc reversals. This section paves the way to EVALUATE1. Let N be a decision network and d an SD candidate node in N . In Subsections 5.1 and 4.1, we have defined the concepts of tail (or downstream component) and body (or ....

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P. P. Shenoy, (1992), Valuation-Based Systems for Bayesian Decision Analysis, Operations research, 40, No. 3, pp. 463-484.

....nodes. This may imply substantial speed up of computation. EVALUATE1 is designed for dealing with multiple value nodes. 7.2. Other approaches This subsections examines the approaches by Howard and Matheson [10] Shachter [26] Ndilikilikesha [19] Tatman and Shachter [38] Shachter [27] Shenoy [34], Shachter and Peot [29] Shenoy [35] and Cooper [3] 7.2.1. Things that can be said for all Until now, influence diagrams have always been assumed to be no forgetting; there have been no methods for dealing with influence diagrams that violate the no forgetting constraint. Even though several ....

....extent made use of the fact that some decision nodes may be independent of some of their parents, no one has proposed to prune 50 removable arcs at the preprocessing stage. The reason is that pruning arcs from an influence results leads to the violation of the no forgetting constraint. Shenoy [34] and [35] proposes a new representation for decision problems, namely valuation based systems. In this representation, the issue of removable arcs does not occur. We will come back to this point later. Probably because they do not prune removable arcs by preprocessing, none of the previous ....

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P. P. Shenoy, (1990), Valuation-Based Systems for Bayesian Decision Analysis, Working Paper No. 220, Business School, University of Kansas.

....property of com14 piling a theory into a backtrack free (i.e. greedy) theory, and their complexity is dependent on the induced width graph parameter. The algorithms are variations on known algorithms, and, for the most part, are not new in the sense that the basic ideas have existed for some time [8, 34, 31, 50, 28, 39, 32, 3, 45, 46, 48, 47]. Definition 2 (graph concepts) A directed graph is a pair, G = fV; Eg, where V = fX 1 ; Xng is a set of elements and E = f(X i ; X j )jX i ; X j 2 V; i 6= jg is the set of edges. If (X i ; X j ) 2 E, we say that X i points to X j . For each variable X i , the set of parent nodes of X i , ....

....allow efficient algorithms of hypertrees and therefore can benefit from a tree clustering approach was recognized by several works in the last decade. In [38] the connection between optimization and constraint satisfaction and its relationship to dynamic programming is explicated. In the work of [33, 47] and later in [6] an axiomatic framework that characterize tasks that can be solved polynomially over hyper trees, is introduced. Such tasks can be described using combination and projection operators over real valued functions, and satisfy a certain set of axioms. The axiomatic framework [47] was ....

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P.P. Shenoy. Valuation-based systems for bayesian decision analysis. Operations Research, 40:463--484, 1992.

.... the set of informational states for a decision variable may contain impossible configurations i.e. configurations having zero probability; conventional evaluation algorithms computes an optimal strategy for each informational state even though they need not be computed at all[Shachter, 1986] [Shenoy, 1992], Ndilikilikesha, 1994] 1 and [Jensen et al. 1994] Secondly, if the legitimate decision options for a decision variable vary w.r.t. the informational states, we need degenerate value functions having large negative values associated with the illegal decision options since conventional ....

....is predetermined i.e. previous observations and decisions can not influence the temporal order of future decisions and observations. Alternatively, Shenoy, 1995] presents the asymmetric valuation network as an extension of the valuation network used for modelling symmetric decision scenarios[Shenoy, 1992]; the valuation network mainly differs from the influence diagram by not requiring conditional probability functions when specifying the uncertainty. The asymmetric valuation network represents the asymmetry in the decision scenario by indicator functions i.e. the asymmetry is encoded at the ....

Shenoy, P. P. (1992). Valuation-based systems for Bayesian decision analysis. Operations Research, 40(3):463--484.

.... large conditionals during the evaluation since they encode both numeric information and information about asymmetry [Shenoy, 2000] To overcome this problem [Shenoy, 2000] presents the asymmetric valuation network as an extension of the valuation network for modelling symmetric decision problems[Shenoy, 1992]. The asymmetric valuation network uses indicator functions to encode asymmetry, thereby separating it from the numeric information. However, asymmetry is still not represented directly in the model and, as in [Smith et al. 1993] the sequence of observations and decisions is predetermined. 1 ....

Shenoy, P. P. (1992). Valuation-based Systems for Bayesian Decision analysis. Operations Research, 40(3):463-484.

....of CTE was proved for the respective tasks in constraint satisfaction and probabilistic reasoning. The extension to the unified framework is immediate. A more general, axiomatic treatment of this subject, applicable for CTE as well can be found in the work of Shenoy [Shafer and Shenoy, 1990, Shenoy, 1992, Schmidt and Shenoy, 1998] For clarity and completeness we can show explicitly Theorem 3.2 (Correctness and completeness) Assume that the combination operator N i and marginalization operator Y satisfy the following properties: 1. Associativity: f N g = g N f 2. Commutativity: f N ....

....bucket tree by merging adjacent nodes. For illustration see Figure 7. 6 Conclusions By its nature the work here is related to all the work in the past two decades on tree decompositions for specific tasks, to which we referred sporadically throughout the paper. Unifying framework were presented [Shenoy, 1992, Shenoy, 1996, Bistarelli et al. 1997] The work here put some of these schemes and formalisms together. The main novelty of the paper is in extending the general variable elimination algorithm called bucket elimination, into a two phase algorithm along a buckettree making explicit the ....

P.P. Shenoy. Valuation-based systems for bayesian decision analysis. Operations Research, 40:463--484, 1992.

....Bajers Vej 7G, DK 9220 Aalborg, Denmark. 1 1 Introduction Influence diagrams (Howard and Matheson 1984) are compact representations of decision problems under uncertainty, and local computation algorithms for solving these have been developed, for example, by Olmsted (1983) Shachter (1986) Shenoy (1992) and Jensen et al. 1994) In the present article we relax the 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 ....

....1 given by #W 1 W = 0 X WnW1 p W ; P WnW1 p W uW P WnW 1 p W 1 A : The division operation in the utility part is necessary to preserve expected utilities. The convention 0=0 = 0 has been used here and throughout. The notion of potential and combination are similar to what is used in Shenoy (1992), Jensen et al. 1994) and Cowell et al. 1999) Marginalization is what these authors have termed summarginalization. The first axiom amounts to combination satisfying the properties of a commutative semigroup, i.e. being associative and commutative: Lemma 2 (Commutativity and associativity of ....

Shenoy, P. P. (1992). Valuation-based systems for Bayesian decision analysis. Operations Research, 40, 463--84.

....responses as mentioned in section 4.2.3. MPD PD RP RP FA FA FA Y Y Y N Y Y N N N N N Y Y N Decision Tree Influence Diagram UF MPD UD PD PS FA RP UR Figure 8: Decision tree and Influence diagram representation of the pregnancy diagnosis and replacement problem. Shenoy (1992) proposed another algorithm that gave the solution to the influence diagram without disrupting the structure of the diagram. Then Jensen et al. 1994) showed how a similar approach could be incorporated within the general framework of Bayesian Networks. This approach has been implemented in the ....

Shenoy, P.P. 1992. Valuation-based systems for Bayesian decision analysis. Operations Research 40, 463-484.

....of temporal independence in IDs. The advantages of having an operational characterization of temporal independence are twofold. To take the most obvious advantage first. When a computer system solves an ID it basicly eliminates the variables in reverse temporal order (see [Shachter, 1986] [Shenoy, 1992], Jensen et al. 1994] and [Zhang, 1998] eliminating a variable produces a table (function) over all non eliminated neighbours. However, the reverse temporal order of elimination has a tendency to create very large tables (usually much larger than for Bayesian networks of the same complexity) ....

Shenoy, P. P. (1992). Valuation-based systems for Bayesian decision analysis. Operations Research, 40(3):463--484.

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Shenoy, P. P. (1992), "Valuation-based systems for Bayesian decision analysis," Operations Research, 40(3), 463-484.

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Prakash P. Shenoy. 1991. Valuation-based systems for Bayesian decision analysis. Operations Research, 40:463--484.

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Shenoy, P. P. (1992). Valuation-Based Systems for Bayesian Decision Analysis. Operations Research, 40(3):463-484.

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P.P. Shenoy, "Valuation-based systems for Bayesian decision analysis," em Operations Research, 40 (1992): 463-484.

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P.P. Shenoy. Valuation-based systems for bayesian decision analysis. Operations Research, 40:463-- 484, 1992.

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P.P. Shenoy. Valuation-based systems for bayesian decision analysis. Operations Research, 40:463--484, 1992.

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P. P. Shenoy, (1992), Valuation-Based Systems for Bayesian Decision Analysis, Operations research, 40, No. 3, pp. 463-484.

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P. P. Shenoy, (1990), Valuation-Based Systems for Bayesian Decision Analysis, Working Paper No. 220, Business School, University of Kansas.

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Shenoy, P. 1992. Valuation-based systems for bayesian decision analysis. Operations Research 40:463--484.

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P.P. Shenoy. Valuation-based systems for bayesian decision analysis. Operations Research, 40:463--484, 1992.

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P. P. Shenoy (1992), Valuation-based systems for Bayesian decision analysis, Operations Research, 40(3), pp. 463-484.

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P. P. Shenoy (1992), Valuation-based systems for Bayesian decision analysis, Operations Research, 40(3), pp. 463-484.

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P. P. Shenoy, (1992), Valuation-Based Systems for Bayesian Decision Analysis, Operations research, 40, No. 3, pp. 463-484.

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P.P. Shenoy. Valuation-based systems for bayesian decision analysis. Operations Research, 40:463--484, 1992.

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