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105
Axioms for probability and belieffunction propagation
 Uncertainty in Artificial Intelligence
, 1990
"... In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We ..."
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Cited by 137 (17 self)
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In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework. 1.
From Influence Diagrams to Junction Trees
 PROCEEDINGS OF THE TENTH CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 1994
"... We present an approach to the solution of decision problems formulated as influence diagrams. This approach involves a special triangulation of the underlying graph, the construction of a junction tree with special properties, and a message passing algorithm operating on the junction tree for comput ..."
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Cited by 111 (15 self)
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We present an approach to the solution of decision problems formulated as influence diagrams. This approach involves a special triangulation of the underlying graph, the construction of a junction tree with special properties, and a message passing algorithm operating on the junction tree for computation of expected utilities and optimal decision policies.
Processor verification using efficient reductions of the logic of uninterpreted functions to propositional logic
 ACM Transactions on Computational Logic
, 1999
"... The logic of equality with uninterpreted functions (EUF) provides a means of abstracting the manipulation of data by a processor when verifying the correctness of its control logic. By reducing formulas in this logic to propositional formulas, we can apply Boolean methods such as Ordered Binary Deci ..."
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Cited by 90 (24 self)
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The logic of equality with uninterpreted functions (EUF) provides a means of abstracting the manipulation of data by a processor when verifying the correctness of its control logic. By reducing formulas in this logic to propositional formulas, we can apply Boolean methods such as Ordered Binary Decision Diagrams (BDDs) and Boolean satisfiability checkers to perform the verification. We can exploit characteristics of the formulas describing the verification conditions to greatly simplify the propositional formulas generated. We identify a class of terms we call "pterms" for which equality comparisons can only be used in monotonically positive formulas. By applying suitable abstractions to the hardware model, we can express the functionality of data values and instruction addresses flowing through an instruction pipeline with pterms. A decision procedure can exploit the restricted uses of pterms by considering only "maximally diverse" interpretations of the associated function symbols...
Perspectives on the Theory and Practice of Belief Functions
 International Journal of Approximate Reasoning
, 1990
"... The theory of belief functions provides one way to use mathematical probability in subjective judgment. It is a generalization of the Bayesian theory of subjective probability. When we use the Bayesian theory to quantify judgments about a question, we must assign probabilities to the possible answer ..."
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Cited by 86 (7 self)
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The theory of belief functions provides one way to use mathematical probability in subjective judgment. It is a generalization of the Bayesian theory of subjective probability. When we use the Bayesian theory to quantify judgments about a question, we must assign probabilities to the possible answers to that question. The theory of belief functions is more flexible; it allows us to derive degrees of belief for a question from probabilities for a related question. These degrees of belief may or may not have the mathematical properties of probabilities; how much they differ from probabilities will depend on how closely the two questions are related. Examples of what we would now call belieffunction reasoning can be found in the late seventeenth and early eighteenth centuries, well before Bayesian ideas were developed. In 1689, George Hooper gave rules for combining testimony that can be recognized as special cases of Dempster's rule for combining belief functions (Shafer 1986a). Similar rules were formulated by Jakob Bernoulli in his Ars Conjectandi, published posthumously in 1713, and by JohannHeinrich Lambert in his Neues Organon, published in 1764 (Shafer 1978). Examples of belieffunction reasoning can also be found in more recent work, by authors
A simple approach to Bayesian network computations
, 1994
"... The general problem of computing posterior probabilities in Bayesian networks is NPhard (Cooper 1990). However efficient algorithms are often possible for particular applications by exploiting problem structures. It is well understood that the key to the materialization of such a possibility is to ..."
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Cited by 82 (8 self)
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The general problem of computing posterior probabilities in Bayesian networks is NPhard (Cooper 1990). However efficient algorithms are often possible for particular applications by exploiting problem structures. It is well understood that the key to the materialization of such a possibility is to make use of conditional independence and work with factorizations of joint probabilities rather than joint probabilities themselves. Different exact approaches can be characterized in terms of their choices of factorizations. We propose a new approach which adopts a straightforward way for factorizing joint probabilities. In comparison with the clique tree propagation approach, our approach is very simple. It allows the pruning of irrelevant variables, it accommodates changes to the knowledge base more easily. it is easier to implement. More importantly, it can be adapted to utilize both intercausal independence and conditional independence in one uniform framework. On the other hand, clique tree propagation is better in terms of facilitating precomputations.
A Sufficiently Fast Algorithm for Finding Close to Optimal Junction Trees
, 1996
"... An algorithm is developed for finding a close to optimal junction tree of a given graph G. ..."
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Cited by 76 (3 self)
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An algorithm is developed for finding a close to optimal junction tree of a given graph G.
Positive definite completions of partial Hermitian matrices
 Linear Alg. Its Applic
, 1984
"... The question of which partial Hermitian matrices (some entries specified, some free) may be completed to positive definite matrices is addressed. It is shown that if the diagonal entries are specified and principal minors, composed of specified entries, are positive, then, if the undirected graph of ..."
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Cited by 74 (10 self)
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The question of which partial Hermitian matrices (some entries specified, some free) may be completed to positive definite matrices is addressed. It is shown that if the diagonal entries are specified and principal minors, composed of specified entries, are positive, then, if the undirected graph of the specified entries is chordal, a positive definite completion necessarily exists. Furthermore, if this graph is not chordal, then examples exist without positive definite completions. In case a positive definite completion exists, there is a unique matrix, in the class of all positive definite completions, whose determinant is maximal, and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original
Probabilistic argumentation systems
 Handbook of Defeasible Reasoning and Uncertainty Management Systems, Volume 5: Algorithms for Uncertainty and Defeasible Reasoning
, 2000
"... Different formalisms for solving problems of inference under uncertainty have been developed so far. The most popular numerical approach is the theory of Bayesian inference [42]. More general approaches are the DempsterShafer theory of evidence [51], and possibility theory [16], which is closely re ..."
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Cited by 53 (33 self)
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Different formalisms for solving problems of inference under uncertainty have been developed so far. The most popular numerical approach is the theory of Bayesian inference [42]. More general approaches are the DempsterShafer theory of evidence [51], and possibility theory [16], which is closely related to fuzzy systems.
Approximating Treewidth, Pathwidth, Frontsize, and Shortest Elimination Tree
, 1995
"... Various parameters of graphs connected to sparse matrix factorization and other applications can be approximated using an algorithm of Leighton et al. that finds vertex separators of graphs. The approximate values of the parameters, which include minimum front size, treewidth, pathwidth, and minimum ..."
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Cited by 52 (4 self)
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Various parameters of graphs connected to sparse matrix factorization and other applications can be approximated using an algorithm of Leighton et al. that finds vertex separators of graphs. The approximate values of the parameters, which include minimum front size, treewidth, pathwidth, and minimum elimination tree height, are no more than O(logn) (minimum front size and treewidth) and O(log^2 n) (pathwidth and minimum elimination tree height) times the optimal values. In addition, we show that unless P = NP there are no absolute approximation algorithms for any of the parameters.
GAI networks for utility elicitation
 In Proccedings of the Ninth International Conference on the Principles of Knowledge Representation and Reasoning (KR’04
, 2004
"... This paper deals with preference representation and elicitation in the context of multiattribute utility theory under risk. Assuming the decision maker behaves according to the EU model, we investigate the elicitation of generalized additively decomposable utility functions on a product set (GAIdec ..."
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Cited by 43 (10 self)
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This paper deals with preference representation and elicitation in the context of multiattribute utility theory under risk. Assuming the decision maker behaves according to the EU model, we investigate the elicitation of generalized additively decomposable utility functions on a product set (GAIdecomposable utilities). We propose a general elicitation procedure based on a new graphical model called a GAInetwork. The latter is used to represent and manage independences between attributes, as junction graphs model independences between random variables in Bayesian networks. It is used to design an elicitation questionnaire based on simple lotteries involving completely specified outcomes. Our elicitation procedure is convenient for any GAIdecomposable utility function, thus enhancing the possibilities offered by UCPnetworks.