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19
Stable Local Computation with Conditional Gaussian Distributions
 Statistics and Computing
, 1999
"... : This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (1992). The propagation architecture is that of Lauritzen and Spiegelhalter (1988). In addition to the means and ..."
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Cited by 63 (1 self)
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: This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (1992). The propagation architecture is that of Lauritzen and Spiegelhalter (1988). In addition to the means and variances provided by the previous algorithm, the new propagation scheme yields full local marginal distributions. The new scheme also handles linear deterministic relationships between continuous variables in the network specification. The new propagation scheme is in many ways faster and simpler than previous schemes and the method has been implemented in the most recent version of the HUGIN software. Key words: Artificial intelligence, Bayesian networks, CG distributions, Gaussian mixtures, probabilistic expert systems, propagation of evidence. 1 Introduction Bayesian networks have developed into an important tool for building systems for decision support in environments characterized by...
On the Implication Problem for Probabilistic Conditional Independency
, 2000
"... The implication problem is to test whether a given set of independencies logically implies another independency. This problem is crucial in the design of a probabilistic reasoning system. We advocate that Bayesian networks are a generalization of standard relational databases. On the contrary, it ha ..."
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Cited by 35 (30 self)
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The implication problem is to test whether a given set of independencies logically implies another independency. This problem is crucial in the design of a probabilistic reasoning system. We advocate that Bayesian networks are a generalization of standard relational databases. On the contrary, it has been suggested that Bayesian networks are different from the relational databases because the implication problem of these two systems does not coincide for some classes of probabilistic independencies. This remark, however, does not take into consideration one important issue, namely, the solvability of the implication problem.
A Method for Implementing a Probabilistic Model as a Relational Database
 In Eleventh Conference on Uncertainty in Artificial Intelligence
, 1995
"... This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model. ..."
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Cited by 29 (19 self)
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This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model.
Local Computation with Valuations from a Commutative Semigroup
 Annals of Mathematics and Artificial Intelligence
, 1996
"... This paper studies a variant of axioms originally developed by Shafer and Shenoy (1988). It is investigated which extra assumptions are needed to perform the local computations in a HUGINlike architecture (Jensen et al. 1990) or in the architecture of Lauritzen and Spiegelhalter (1988). In particul ..."
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Cited by 28 (8 self)
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This paper studies a variant of axioms originally developed by Shafer and Shenoy (1988). It is investigated which extra assumptions are needed to perform the local computations in a HUGINlike architecture (Jensen et al. 1990) or in the architecture of Lauritzen and Spiegelhalter (1988). In particular it is shown that propagation of belief functions can be performed in these architectures. Keywords: articial intelligence, belief function, constraint propagation, expert system, probability propagation, valuationbased system. 1 Introduction An important development in articial intelligence is associated with an abstract theory of local computation known as the Shafer{Shenoy axioms (Shafer and Shenoy 1988; Shenoy and Shafer 1990). These describe in a very general setting how computations can be performed eciently and locally in a variety of problems, just if a few simple conditions are satised. Even though the axioms were developed to formalize computation with belief functions (Shaf...
A Bayesian Approach to User Profiling In Information Retrieval
 TECHNOLOGY LETTERS
, 2000
"... Numerous probability models have been suggested for information retrieval (IR) over the years. These models have been applied to try to manage the inherent uncertainty in IR, for instance, document and query representation, relevance feedback, and evaluating the effectiveness of IR system. On ..."
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Cited by 10 (2 self)
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Numerous probability models have been suggested for information retrieval (IR) over the years. These models have been applied to try to manage the inherent uncertainty in IR, for instance, document and query representation, relevance feedback, and evaluating the effectiveness of IR system. On the other hand, Bayesian networks have become an established probabilistic framework for uncertainty management in artificial intelligence. In this
On Undirected Representations of Bayesian Networks
 ACM SIGIR Workshop on Mathematical/Formal Models in Information Retrieval
, 2001
"... Empirical studies clearly demonstrate the effectiveness of the nested jointree (NJT) representation in probabilistic inference. A NJT is a traditional Markov network (MN) together with a possible local MN nested in each clique. These nested MNs can themselves contain other nested MNs in a recu ..."
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Cited by 7 (6 self)
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Empirical studies clearly demonstrate the effectiveness of the nested jointree (NJT) representation in probabilistic inference. A NJT is a traditional Markov network (MN) together with a possible local MN nested in each clique. These nested MNs can themselves contain other nested MNs in a recursive manner. However, the NJT representation is not necessarily a faithful representation of a given Bayesian network (BN).
Probabilistic Reasoning in Bayesian Networks: A Relational Database Approach
 Sixteenth Canadian Conference on Artificial Intelligence
, 2003
"... Probabilistic reasoning in Bayesian networks is normally conducted on a junction tree by repeatedly applying the local propagation whenever new evidence is observed. In this paper, we suggest to treat probabilistic reasoning as database queries. We adapt a method for answering queries in databas ..."
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Cited by 6 (3 self)
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Probabilistic reasoning in Bayesian networks is normally conducted on a junction tree by repeatedly applying the local propagation whenever new evidence is observed. In this paper, we suggest to treat probabilistic reasoning as database queries. We adapt a method for answering queries in database theory to the setting of probabilistic reasoning in Bayesian networks. We show an e#ective method for probabilistic reasoning without repeated application of local propagation whenever evidence is observed.
Automated Database Schema Design Using Mined Data Dependencies
 J. Amer. Soc. Inform. Sci
, 1998
"... Data dependencies are used in database schema design to enforce the correctness of a database as well as to reduce redundant data. These dependencies are usually determined from the semantics of the attributes and are then enforced upon the relations. This paper describes a bottomup procedure for d ..."
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Cited by 6 (0 self)
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Data dependencies are used in database schema design to enforce the correctness of a database as well as to reduce redundant data. These dependencies are usually determined from the semantics of the attributes and are then enforced upon the relations. This paper describes a bottomup procedure for discovering multivalued dependencies (MVDs) in observed data without knowing `a priori the relationships amongst the attributes. The proposed algorithm is an application of the technique we designed for learning conditional independencies in probabilistic reasoning. A prototype system for automated database schema design has been implemented. Experiments were carried out to demonstrate both the effectiveness and efficiency of our method. 1
On Data and Probabilistic Dependencies
 Proceedings of the 1999 IEEE Canadian Conference on Electrical and Computer Engineering
, 1999
"... Data dependencies have been extensively studied in relational databases as they play a key role in the normalization process. On the other hand, probabilistic reasoning systems would not be practical without the notion of probabilistic conditional independence. In this paper, we present a detailed c ..."
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Cited by 4 (4 self)
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Data dependencies have been extensively studied in relational databases as they play a key role in the normalization process. On the other hand, probabilistic reasoning systems would not be practical without the notion of probabilistic conditional independence. In this paper, we present a detailed comparison of these two types of (in)dependencies. While past research has shown that multivalued dependency is a necessary but not sufficient condition for conditional independence, here we show in particular that functional dependency is a sufficient but not necessary condition for conditional independence.
An algebraic study of argumentation systems and evidence theory
, 1995
"... Argumentation systems permit to nd arguments in favour and against hypotheses. And these hypotheses can be accepted as true or must be refuted as false according to whether the arguments supporting or refuting them are considered to be valid. Possibly the likelihood of arguments can be measured by p ..."
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Cited by 2 (1 self)
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Argumentation systems permit to nd arguments in favour and against hypotheses. And these hypotheses can be accepted as true or must be refuted as false according to whether the arguments supporting or refuting them are considered to be valid. Possibly the likelihood of arguments can be measured by probabilities. Then argumentation systems permit to de ne numerical degrees of support of hypotheses as the probability that arguments supporting the hypotheses are true. Similarly, numerical degrees of plausibility ofhypotheses can be de ned as the probability that arguments refuting the hypotheses do not hold. These probabilistic argumentation systems lead then to a DempsterShafer theory of evidence. In this paper rst an algebraic theory of argumentation systems is developped based on general logical consequence relations and the notion of an allocation of support. In particular a computational theory for argumentation systems using local computations on hypertrees is studied on the fundaments of Shafer's paper \An axiomatic study of computations in hypertrees&quot;. This is then extended to probabilistic argumentation