R.D. Shachter, B. D'Ambrosio, and B.A. Del Favro, "Symbolic probabilistic inference in belief networks," Automated Reasoning (1990): 126-131. In Operations Research Vol. 36, No.4, 198b.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....ON HYPERTREE ORGANIZATION A. Classification of loops The difficulty of coherent inference in multiply connected graphical models (those with loops) of probabilistic knowledge is well known and many inference algorithms have been proposed. Those based on message passing, e.g. 20] 14] 10] [23], 4] all convert a multiply connected network into a tree. However, no formal arguments can be found, e.g. in [20] 9] 18] 3] which demonstrate convincingly that message passing cannot be made coherent in multiply connected networks. This leaves the question whether it is impossible to ....

R.D. Shachter, B. D'Ambrosio, and B.A. Del Favero. Symbolic probabilistic inference in belief networks. In Proc. 8th Natl. Conf. on Artificial Intelligence, pages 126--131, 1990.

....elimination ordering is NP complete. Symbolic probabilistic inference (SPI) views probabilistic inference as a combinatorial optimization problem, the optimal factoring problem. Probabilistic inference is the problem of finding an optimal factoring given a set of probabilistic distributions [SD90, LD94]. SPI is symbolic and querydriven. Differential approach compiles a Bayesian network into a multivariate polynomial and then computes the partial derivatives of this polynomial with respect to each variable [Da00] Once such derivatives aremadeavailable,onecancomputeanswerstoavery large class of ....

R.D.Shachter,B.D'Ambrosio,andB.D.Del Favero. Symbolic probabilistic inference in belief networks, Proc. 8th National Conference on Artificial Intelligence, MIT Press, Boston, pp. 126---131, 1990.

....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 , ....

....Figure 17. We conclude: Theorem 3 Algorithm elim bel computes the posterior belief P (x 1 je) for any given ordering of the variables which is initiated by X 1 . 2 The peeling algorithm for genetic trees [8] Zhang and Poole s algorithm [51] as well as the SPI algorithm by D Ambrosio et al. [39] are all variations of elim bel. Decimation algorithms in statistical physics are also related and were applied to Boltzmann trees [43] 21 B C D F A G B C D F A G D F B C A (a) b) c) Figure 18: Two orderings of the moral graph of our example problem 4.2 Complexity We see ....

[Article contains additional citation context not shown here]

B. D'Ambrosio R.D. Shachter and B.A. Del Favero. Symbolic probabilistic inference in belief networks. In National Conference on Artificial Intelligence (AAAI'90), pages 126--131, 1990. 50

....to determine the posterior probability of a variable or variables given some observations. In this section we outline a simple algorithm for belief net inference called VE [Zhang and Poole, 1996] or bucket elimination for belief assessment, BEBA [Dechter, 1996] that is based on the ideas of SPI [Shachter et al. 1990] . This is a query oriented algorithm that exploits network structure for efficient inference, similarly to clique tree propagation [Lauritzen and Spiegelhalter, 1988; Jensen et al. 1990] One difference is the factors represent conditional probabilities rather than the marginal probabilities ....

R. D. Shachter, B. D. D'Ambrosio, and B. D. Del Favero. Symbolic probabilistic inference in belief networks. In Proc. 8th National Conference on Artificial Intelligence, pages 126--131, Boston, 1990. MIT Press.

.... and an elimination order of width w, rc takes O(n exp(w log n) time under O(n) space, which is a new complexity result for linear space Bayesian network inference, and takes O(n exp(w) time under O(n exp(w) space, therefore, matching the complexity of clustering [7, 6] and elimination [10, 4, 11] algorithms. 1 rc is also equipped with a formula for computing its average running time under any amount of space. To introduce the key intuition underlying recursive conditioning, we note that the power of conditioning is in its ability to reduce network connectivity. In cutset conditioning, ....

R. Shachter, B.D. D'Ambrosio, and B. del Favero. Symbolic Probabilistic Inference in Belief Networks. In Proc. Conf. on Uncertainty in AI, pages 126-131, 1990.

.... is also known as the loop cutset method [25, 26, 28] The best known fact about this method is its linear space complexity, which is very attractive when compared to the exponential space complexity (in treewidth) of state of the art algorithms based on clustering [19, 30, 18, 17] and elimination [29, 20, 11, 32]. The worst known fact about cutset conditioning is its time complexity, which is exponential in the size of loop cutset. The loop cutset can be quite large, even for networks which can be solved in linear time and space using other methods. There have been improvements and variations on cutset ....

R. Shachter, B.D. D'Ambrosio, and B. del Favero. Symbolic Probabilistic Inference in Belief Networks. In Proc. Conf. on Uncertainty in AI, pages 126-131, 1990.

....table it speci es. The main goal of algorithms for Bayesian networks is to answer such queries without having to construct the table explicitly, which size is exponential in the number of network variables. The main approaches for inference in Bayesian networks are based on variable elimination [24, 8, 25], jointrees [13, 14] or conditioning [22, 12, 9, 5, 6] We present in this paper a new, comprehensive approach to inference in Bayesian networks which rests on compiling the network into a factored polynomial. Given a piece of evidence, the polynomial is then evaluated and its partial derivatives ....

.... x and network parameters f . Given a variable elimination order of induced width w and length n, we show how to compile the polynomial in O(n exp(w) time using a simple variable elimination algorithm. 2. We show how to answer a large number of queries relating to classical inference [13, 15, 8, 25, 24], parameter estimation [23, 19] model validation [4] and sensitivity analysis [18, 2, 3] in constant time once the partial derivatives of the compiled polynomial are computed. 3. We show the following on the complexity of computing the derivatives of such polynomials: a) rst partial ....

[Article contains additional citation context not shown here]

R. Shachter, B.D. D'Ambrosio, and B. del Favero. Symbolic Probabilistic Inference in Belief Networks. In Proc. Conf. on Uncertainty in AI, pages 126-131, 1990.

....indicators x and network parameters f . Given a variable elimination order of with w and length n, we show how to compile the polynomial in O(n exp(w) time using a simple variable elimination algorithm. 2. We show how to answer a large number of queries relating to classical inference [10, 13, 7, 21, 20], parameter estimation [19, 16] model validation [4] and sensitivity analysis [15, 2, 3] in constant time once the partial derivatives of the compiled polynomial are computed. 3. We show the following on the complexity of computing the derivatives of such polynomials: a) rst partial ....

....In Figure 6, where e = a, Pr (b j e) F(e) b ) F(e) 03= 3 = 1 and Pr( b j e) F(e) b ) F(e) 27= 3 = 9. The ability to compute such posteriors eciently is probably the key celebrated property of jointree algorithms [10, 11] as compared to variableelimination algorithms [20, 7, 21]. The latter class of algorithms is much simpler except that they can only compute such posteriors by invoking themselves once for each network variable, leading to a complexity of O(n 2 exp(w) Jointree algorithms can do this in O(n exp(w) however, but at the expense of a more complicated ....

R. Shachter, B.D. D'Ambrosio, and B. del Favero. Symbolic Probabilistic Inference in Belief Networks. In UAI90.

....agent through communication. Then H is connected. 4 On hypertree organization The difficulty of coherent inference in multiply connected (with loops) graphical models of probabilistic knowledge is well known and many inference algorithms have been proposed. Those based on message passing, e.g. [13, 9, 5, 15], all convert a multiply connected network into a tree. However, no formal arguments can be found, e.g. in [13, 4, 11, 1] which demonstrate convincingly that message passing cannot be made coherent in multiply connected networks. This leaves the question whether it is impossible to construct ....

R.D. Shachter, B. D'Ambrosio, and B.A. Del Favero. Symbolic probabilistic inference in belief networks. In Proc. 8th Natl. Conf. on Artificial Intelligence, pages 126--131, 1990.

....followed by knowledge propagation based on a student s answer, an adaptive testing system is produced. 3.1 Knowledge Propagation There are many different algorithms for propagating belief through a Bayes net. The approach in this paper uses Shachter, D Ambrosio and DelFavero s SPI algorithm [5]. While issues of Bayesian belief propagation efficiency are not the primary concern in this paper, the complexity of specifying a Bayes net is. In order for it to be truly useful, a course instructor must be able to construct a Bayes net for a course with a minimal amount of effort. It is hoped ....

R. Shachter, B. D'Ambrosio, and B. DelFavero. Symbolic probabilistic inference in belief networks. In Proceedings Eighth National Conference on AI, pages 126--131. AAAI, August 1990.

....1 s and 0 s. Furthermore, extra links need to be added among the variables which are not mutually independent in order to preserve the dependency properties of the original network. By applying on the original network the efficient algorithms developed for computing the exact belief of a variable [8,9,25], the complete probabilistic information for 9 This condition, P unevaluated L j P r(L j jS e ) 1 Gamma P evaluated L i P r(L i jS e ) has been proved in [20] to be the sufficient condition to stop further evaluation. 24 the sub network can be derived. Subsequently RLCM can be applied ....

....applied to identify the most probable general composite hypotheses which are the same as the MPGE to a given S e in the original network. However, in the process of deriving the probabilistic information relevant to each variable in the sub network, existing efficient algorithms for exact beliefs [8,9,21 25] would still have to deal with exponential number of terms which are not independent from the variables in the sub network with respect to S e . From this it can be seen that the overall computational load remains the same, and the computational load merely shifts from one step to another. ....

R.D. Shachter, B. D'Ambrosio, B.A. Del Favero, "Symbolic Probabilistic Inference in Belief Networks," Proc. of the 8th National Conf. on AI, Boston, Massachusetts, Aug. 1990.

....variables in a Bayesian network are being considered, we refer to such a combination a composite hypothesis. III. Review of relevant research Probabilistic inference in a Bayesian network has been viewed as answering queries relevant to the propositional variables in a Bayesian network [9]; in particular, the likelihoods of the simple or (local) composite hypotheses in the presence of an evidence 2 . Various inference algorithms were developed elsewhere and the details were in [2 3,5,10 19] To date, the most efficient computational method to deal with a simple hypothesis has a ....

R.D. Shachter, B. D'Ambrosio, B.A. Del Favero, "Symbolic Probabilistic Inference in Belief Networks," Proc. of the 8th National Conf. on AI, pp. 126-131, Boston, Massachusetts, Aug. 1990.

....the unobserved variables, so, if XO = xO is the observed evidence, the goal is to obtain P (X i jx O ) for every X i 2 X U n XO . Trying to solve this problem by applying Bayes rule directly is intractable even for a little number of variables. In the last years many algorithms ( 20] 21] 1] [22], 23] have been proposed to solve this problem (in an exact way) by taking advantage of the conditional independences among the variables given by the structure of the graph. These algorithms are called propagation algorithms, because the computations are performed locally, and the information ....

R.D. Shachter, B.D. D'Ambrosio, and B.D. Del Favero, "Symbolic probabilistic inference in belief networks," in 8th National Conference on Artificial Intelligence, Boston, 1990, pp. 126--131, MIT Press.

.... ) w n w O( n exp( w n Same as worst case Elimination Conditioning Average time Space worst case better than exp( n ) O( Worst case time knowledge compilation one solution Output Figure 12: Comparing elimination and conditioning basic ideas have existed for some time [8, 35, 33, 49, 30, 39, 34, 3, 45, 46, 48, 47]. What we are presenting here is a syntactic and uniform exposition emphasizing these algorithms form as a straightforward elimination algorithm. The presentation allows ideas and techniques to flow across the boundaries between areas of research. In particular, having noted that elimination ....

....is described in Figure 17. Theorem 3 Algorithm elim bel compute the posterior belief P (x 1 je) for any given ordering of the variables which is initiated by X 1 . Both the peeling algorithm for genetic trees [8] Zhang and Poole s algorithm [50] and the SPI algorithm by D ambrosio et.al [39] are variations of elim bel. Decimation algorithms in statistical physics are also related and were applied to Boltzmann trees [43] 21 Algorithm elim bel Input: A belief network BN = fP 1 ; Png; an ordering of the variables, d = X 1 ; Xn ; evidence e. Output: The belief in X 1 = x ....

[Article contains additional citation context not shown here]

B. D'Ambrosio R.D. Shachter and B.A. Del Favero. Symbolic probabilistic inference in belief networks. In National Conference on Artificial Intelligence (AAAI90), pages 126--131, 1990.

....to determine the posterior probability of a variable or variables given some observations. In this section we outline a simple algorithm for belief net inference called VE [Zhang and Poole, 1996] or bucket elimination for belief assessment, BEBA [Dechter, 1996] that is based on the ideas of SPI [Shachter et al. 1990] . This is a query oriented algorithm that exploits network structure for efficient inference, similarly to clique tree propagation [Lauritzen and Spiegelhalter, 1988; Jensen et al. 1990] One difference is the factors represent conditional probabilities rather than the marginal probabilities ....

R. D. Shachter, B. D. D'Ambrosio, and B. D. Del Favero. Symbolic probabilistic inference in belief networks. In Proc. 8th National Conference on Artificial Intelligence, pages 126--131, Boston, 1990. MIT Press.

....did not really use the direction of the links in the network. By standard we mean the Lauritzen Spiegelhalter (Lauritzen Spiegelhalter 1988) the Shafer Shenoy (Shafer Shenoy 1990) and the Hugin (Jensen, Lauritzen Olesen 1990) algorithms and the various variations over these algorithms ( (Shachter 1990) and (Jensen 1995) These algorithms build a secondary structure (a junction tree or a join tree) by triangulating the (moralized) network. This structure can be used for propagation for all information scenaria. Therefore, the algorithms do not exploit independences induced by the evidence. ....

....A is instantiated and no evidence has been entered to DAG 4 , then it is only necessary to send messages down to DAG 4 . We may relax the requirement to the updating algorithm such that we are only interested in updated probabilities for a very small set of variables. In that case the SPI method (Shachter, D Ambrosio DelFavero 1990) and the bucket sort algorithm (Dechter 1996) can utilize specific independences, as they consist of a collect operation only, where the variables are successively eliminated by multiplying the functions involving A (say) and marginalizing A out of this product. These methods, however, are not ....

Shachter, R., D'Ambrosio, B. & DelFavero, B. (1990), Symbolic probabilistic inference in belief networks, in `Proceedings Eighth National Conference on AI', pp. 126--131.

....as the sum of x and all incoming numbers except that from V . The sum can now be retrieved from the root. Next, we call DistributeMessage at the same root (c) The sum can now be retrieved from any node. 3 Probability propagation in JTs Various methods for inference in BNs have been constructed [6, 1, 4, 8, 9, 2]. Several [4, 9, 2] use a junction tree (JT) as runtime structure. We review how to convert a BN into a JT and then consider two of them. 3.1 Conversion of a BN into a JT A BN S is a triplet (N; D;P ) where N is a set of variables, D is a DAG whose nodes are labeled by elements of N , and P is a ....

R.D. Shachter, B. D'Ambrosio, and B.A. Del Favero. Symbolic probabilistic inference in belief networks. In Proc. 8th Natl. Conf. on Artificial Intelligence, pages 126--131, 1990.

....did not really use the direction of the links in the network. By standard we mean the LauritzenSpiegelhalter [Lauritzen and Spiegelhalter, 1988] the Shafer Shenoy [Shafer and Shenoy, 1990] and the Hugin [Jensen et al. 1990] algorithms and the various variations over these algorithms ( [Shachter, 1990] and [Jensen, 1995] These algorithms build a secondary structure (a junction tree or a join tree) by triangulating the (moralized) network. This structure can be used for propagation for all information scenaria. Therefore, the algorithms do not exploit independences induced by the evidence. ....

....A is instantiated and no evidence has been entered to DAG 4 , then it is only necessary to sent messages down to DAG 4 . We may relax the requirement to the updating algorithm such that we are only interested in updated probabilities for a very small set of variables. In that case the SPI method [Shachter et al. 1990] and the bucket sort algorithm [Dechter, 1996] can utilize specific independences, as they consist of a collect operation only, where the variables are successively eliminated by multiplying the functions involving A (say) and marginalizing A out of this product. These methods, however, are not ....

Shachter, R., D'Ambrosio, B., and DelFavero, B. (1990). Symbolic probabilistic inference in belief networks. In Proceedings Eighth National Conference on AI, pages 126--131.

....The computational work needed to perform this on line evaluation is so straightford that it lends itself to easy implementations on different software and hardware platforms. This approach shares some commonality with other methods that symbolically manipulate probability expressions, like SPI [3, 5]; it differs with SPI on the objective of such manipulations and, hence, on the results obtained. SPI explicates the notion of an arithmentic expression to state that belief network inference can be viewed as an expression factoring operation. This allows results from optimization theory to be ....

R. Shachter, B.D. D'Ambrosio, and B. del Favero. Symbolic Probabilistic Inference in Belief Networks. In Proc. Conf. on Uncertainty in AI, pages 126--131, 1990.

....independence models such as noisy OR gates, noisy MAXgates, noisy AND gates, and noisy adders as special cases. The method is based on the following observation. A BN can be viewed as representing a factorization of a joint probability into the multiplication of a list of conditional probabilities (Shachter et al. 1990; Zhang Poole, 1994; Li D Ambrosio, 1994) The type of causal independence studied in this paper leads to further factorization of the conditional probabilities (Section 5) A finer grain factorization of the joint probability is obtained as a result. We propose to extend exact inference ....

....by causal independence. The state of art exact inference algorithm is called clique tree propagation (CTP) Lauritzen Spiegelhalter, 1988; Jensen et al. 1990; Shafer Shenoy, 1990) This paper proposes another algorithm called variable elimination (VE) Section 3) that is related to SPI (Shachter et al. 1990; Li D Ambrosio, 1994) and extends it to make use of the finer grain factorization (see Sections 6, 7, and 8) Rather than compiling to a secondary structure and finding the posterior probability for each variable, VE is query oriented; it needs only that part of the network relevant to the ....

[Article contains additional citation context not shown here]

Shachter, R. D., D'Ambrosio, B. D., & Del Favero, B. D. (1990). Symbolic probabilistic inference in belief networks. In Proc. 8th National Conference on Artificial Intelligence, pp. 126--131 Boston. MIT Press.

....Arc Reversal General method for solving Influence diagrams: Sha86] Sha90] FB93] BF91] Mus93] 2.2.5 Symbolic Solution Surprisingly, some good results have emerged by symbolically manipulating equations defining a joint probability distribution, much like Mathematica might do. CF91] SDD90] D A90] D A94] LS88, Comments by W. S. Kendall] CGH95] 2.3 Exact Optimization Finding the best (highest probability) configuration. 2.3.1 Junction Tree Propagation Max propagation: DDP90] Daw92] 2.3.2 Linear Programming Formalizations as linear or non linear programming problems: ....

Ross D. Shachter, Bruce D'Ambrosio, and Brendan A. Del Favero. Symbolic probabilistic inference in belief networks. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 126--131. MIT Press, 1990.

....1 Introduction The problem of probability propagation is defined as the process of calculating the probability values of some variables in a dependence graph, given a set of observed variables. Many algorithms have been proposed in the last years to solve this problem in an exact way [13, 14, 17, 19, 20, 21, 24]. These methods take advantage of conditional independences among the variables given by the structure of the network, to do the propagation by local computations. Although they give exact results, all these algorithms are NP hard [5] in the worst case. So, if the network is complicate enough, ....

....degree of independence, but with a higher computational cost. In this paper we study a general class of importance sampling algorithms, presented in [11] They perform making a first approximate propagation based on the concept of node removal [24] similar to D Ambrosio s symbolic propagation [21]. The results obtained from this first propagation are improved by sampling the obtained functions. Bouckaert [1] and Bouckaert, Castillo and Guti errez [2] developed a stratified sampling scheme for probability propagation. It performs well, but when the network is too complex, precision problems ....

R.D. Shachter, B. D'Ambrosio, B.A. Del Favero (1990) Symbolic probabilistic inference in belief networks. Proceedings of the AAAI'90 Conference, Vol.1, 126-131.

....) Partition the conditional probability matrices fP i g into buckets. In the bucket of X i put all the matrices mentioning X i that do not mention any variable higher in the ordering. The procedure has backward and forward parts and is justified by the following symbolic manipulation (see also [ Shac 90 ] 1) Backward part. Consider variable Xn first (remember x i = x 1 ; x i ) M = max xn P (x) max xn Gamma1 max xn Pi n i=1 P (x i jx pa i ) All the expressions that do not mention Xn can be migrated to the left of the maximization on Xn since, relative to Xn , they are ....

R.D. Shachter, B. D'Ambrosio, and B.A. Del Favro, "Symbolic probabilistic inference in belief networks," Automated Reasoning (1990): 126-131. In Operations Research Vol. 36, No.4, 198b.

....with other known methods. 1 INTRODUCTION Probability propagation in belief networks consists on updating the probability values of the variables in a dependence graph, given some variables that have been observed. Different exact methods have been developed for this purpose in the last years [11, 13, 15, 16, 17, 20]. In general, it can be said that they take advantage of conditional independences among variables expressed by the graph, to develope a local propagation algorithm. Shachter, Andersen and Szolovits showed how these methods can be included inside a global framework based on the concept of cluster ....

....of independence, but with a higher computational cost. In this paper we consider a general class of importance sampling algorithms. The basic idea is to make a previous approximated propagation, following the concept of node removal [20] very similar to the symbolic propagation due to D Ambrosio [17] (section 2) and then improve it by sampling the obtained functions. Node removal is done in two steps: firstly, combining the functions associated with the node to be removed, and secondly, marginalizing the resulting function deleting such variable. The main algorithm is presented in section ....

R.D. Shachter, B. D'Ambrosio, B.A. Del Favero (1990) Symbolic probabilistic inference in belief networks. Proceedings of the AAAI'90 Conference, Vol.1, 126-131.

....needed to perform this on line evaluation is so straightforward that it lends itself to easy implementations on different software and hardware platforms. This approach shares some commonality with other methods that symbolically manipulate probability expressions, like SPI (Li D Ambrosio, 1994; Shachter, D Ambrosio, del Favero, 1990); it differs from SPI on the objective of such manipulations and, hence, on the results obtained. SPI explicates the notion of an arithmetic expression to state that belief network inference can be viewed as an expression factoring operation. This allows results from optimization theory to be ....

....Center. Special thanks to Jack Breese, Bruce D Ambrosio and to the anonymous reviewers for their useful comments on earlier drafts of this paper. 11. We have shown how clustering and conditioning algorithms can be used for Q DAG generation, but other algorithms such as SPI (Li D Ambrosio, 1994; Shachter et al. 1990) can be used as well. A Practical Paradigm for Implementing Belief Network Inference Appendix A. Proof of Theorem 1 Without loss of generality, we assume in this proof that all variables are declared as evidence variables. To prove this soundness theorem, all we need to show is that each Q DAG ....

Shachter, R., D'Ambrosio, B., & del Favero, B. (1990). Symbolic Probabilistic Inference in Belief Networks. In Proc. Conf. on Uncertainty in AI, pp. 126--131.

....provide computational leverage in computing marginal probabilities and conditional probabilities. Rather than globally enumeratng possible combination of variable values, local computation and propagation exploiting dependency and result in much better computational efficiency [JLO90] LS88] SDDF90] AWFA87] 8.5 Decomposition Theory in Relational Databases The decomposition theory for relational databases provides an analogy to the decomposition approach for planning under uncertainty in this thesis. Dependencies among domain features play an important role in decomposition theory for ....

Ross D. Shachter, Bruce D'Ambrosio, and Brendan A. Del Favero. Symbolic probabilistic inference in belief networks. In Proceedings AAAI-90, pages 126--131. AAAI, 1990.

....reason for abandoning the two phase approach might be that people believe that direct evaluation is more efficient. However, all those algorithms that evaluate influence diagrams directly suffer from a common shortcoming in handling asymmetric decision problems (Covaliu and Oliver 1992, Fung and Shachter 1990, Phillips 1990, Shachter 1986, Smith et al. 1993) Decision problems are usually asymmetric in the sense that the set of possible outcomes of a random variable may vary depending on different conditioning states, and the set of legitimate alternatives of a decision variable may vary depending on ....

....d is removed by maximization A New Method for Influence Diagram Evaluation 11 Other developments. Influence diagrams are closely related to Bayesian nets (Pearl 1988) Quite a few algorithms have been developed in the literature (Jensen et al. 1990, Lauritzen and Spiegelhalter 1988, Pearl 1988, Shachter et al. 1990, Zhang and Poole 1992a) for computing marginal probabilities and posterior probabilities in Bayesian nets. Thus, it is natural to ask whether we can make use of these Bayesian net al..gorithms for influence diagram evaluation. This problem is examined in (Cooper 1988, Ndilikilikesha 1991, Shachter ....

[Article contains additional citation context not shown here]

Shachter, R. D., B. D'Ambrosio, and B. A. Del Favero. 1990. Symbolic probabilistic inference in belief networks. In Proc. of AAAI-90, pages 126--131.

.... [123, 124] Shachter later extended this method to handle experimental evidence by including evidence reversal operations [125] Yet another different class of approaches to probabilistic inference was introduced by D Ambrosio and his colleagues as the Symbolic Probabilistic Inference (SPI) method [36, 37, 121]. SPI performs only the calculations that are required to respond to a given query, as opposed to, say, Pearl s belief propagation algorithm [110] in which all local distributions are computed, regardless of their relevance to the query at hand. Several extensions of SPI have also been ....

R. Shachter, B. D'Ambrosio, and B.A. del Favero. Symbolic probabilistic inference in belief networks. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 126--131, August 1990.

....by knowledge propagation based on a student s answer, an adaptive testing system can be produced. 3.2.2 Knowledge Propagation There are many different algorithms for propagating belief through a Bayes net. The approach in this thesis uses Shachter, D Ambrosio, and DelFavero s SPI algorithm [Shachter et al. 1990]. Both the issues of Bayesian belief propagation efficiency and the complexity of specifying a Bayesian network are of primary concern in this thesis. In order for this approach to be truly useful, a course instructor must be able to construct a Bayes net for a course with a minimal amount of ....

Shachter, R., D'Ambrosio, B., and DelFavero, B. (1990). Symbolic probabilistic inference in belief networks. In Proceedings Eighth National Conference on AI, pages 126--131. AAAI.

....network inference is to determine the posterior probability of variables given some observations. In this section we outline a simple algorithm for Bayesian net inference called VE (Zhang Poole 1996) or bucket elimination for belief assessment (Dechter 1996) and is closely related to SPI (Shachter, D Ambrosio Del Favero 1990). This is a query oriented algorithm that exploits network structure for efficient inference, similarly to clique tree propagation (Lauritzen Spiegelhalter 1988, Jensen, Lauritzen Olesen 1990) One difference is the factors represent conditional probabilities rather than the marginal ....

Shachter, R. D., D'Ambrosio, B. D. & Del Favero, B. D. (1990). Symbolic probabilistic inference in belief networks, Proc. 8th National Conference on Artificial Intelligence, MIT Press, Boston, pp. 126--131.

....monitored. Finally, we motivated the notion of an alert s urgency, and we captured this notion within our framework: We provided an action based definition of urgency, Methods for exact inference include conditioning [10, 37, 39] clustering [21, 22, 27, 48] and symbolic probabilistic inference [29, 46]. 15 and we developed, from our temporally extended decision model, a quantitative measure of this urgency. We propose that our alarm framework can guide the design of effective alarm systems in a variety of domains, and that such systems can be realized by invoking appropriate engineering ....

Ross Shachter, Bruce D'Ambrosio, and Brendan Del Favero. Symbolic probabilistic inference in belief networks. In Proceedings of the 8th National Conference on AI, pages 126--131, Boston, Mass., August 1990.

No context found.

R.D. Shachter, B. D'Ambrosio, and B.A. Del Favro, "Symbolic probabilistic inference in belief networks," Automated Reasoning (1990): 126-131. In Operations Research Vol. 36, No.4, 198b.

No context found.

R. D. Shachter, B. D'Ambrosio, and B. A. Del Favero (1990), Symbolic Probabilistic Inference in Belief Networks, in AAAI-90, pp. 126-131.

No context found.

R. D. Shachter, B. D'Ambrosio, and B. D. Del Favero. Symbolic probabilistic inference in belief networks, Proc. 8th National Conference on Artificial Intelligence, MIT Press, Boston, pp. 126---131, 1990.

No context found.

Ross D. Shachter, Brendan A. Del Favero, and Bruce D'Ambrosio. Symbolic probabilistic inference in belief networks. In AAAI, pages 126--131, 1990.

No context found.

Shachter, R., D'Ambrosio, B., and Del Favero, B., Symbolic probabilistic inference in belief networks, in Proceedings of the 8th National Conference on AI, Boston, Mass., 126#131, 1990.

No context found.

B. D'Ambrosio R.D. Shachter and B.A. Del Favro. Symbolic probabilistic inference in belief networks. Automated Reasoning, pages 126--131, 1990.

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