S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 , ....

....subset of hypothesis variables (known as map and analyzed in the next section) the mpe is close enough and is often used in applications. Researchers have investigated various approaches to finding the mpe in a belief network [34, 35, 36] Recent proposals include best first search algorithms [48] and algorithms based on linear programming [41] The problem is to find x such that P (x ) max x P (x; e) max x Pi i P (x i ; ejx pa i ) where x = x 1 ; xn ) and e is a set of observations, on subsets of the variables. Computing for a given ordering X 1 ; Xn , can be ....

S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer (Eds.), Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.

....our probabilistic estimates, which de Kleer cannot do. One of the features of our work is that finding minimal conflicts is not essential to the correctness of the program, but only to the efficiency. Thus we can explore the idea of saving time by finding useful, but nonminimal conflicts quickly. Shimony and Charniak [1990] , Poole [1992a] and D Ambrosio [1992] haveproposed back chaining search algorithms for Bayesian networks. None of these are nearly as efficient as the one presented here. Even if we consider finding the single most normal world, the algorithm here corresponds to forward chaining on definite ....

S. E.Shimony and E.Charniak. A new algorithm for finding MAP assignments to belief networks. In Proc. Sixth Conf. on Uncertainty in Artificial Intelligence, pages 98--103, Cambridge, Mass., July 1990.

....used for the resulting singly connected networks. Instead of enumerating the variables of the cutsets, we enumerate all of the variables. This makes the algorithm much simpler, and allows for fast processing. Bounded conditioning has no analogue to the conflicts of this paper. Shimony and Charniak [39], Poole [32] and D Ambrosio [4] have proposed back chaining search algorithms for Bayesian networks. None of these are nearly as efficient as the one presented here. Even if we consider finding the single most normal world, the algorithm here corresponds to forward chaining on definite clauses ....

S. E. Shimony and E. Charniak. A new algorithm for finding MAP assignments to belief networks. In Proc. Sixth Conf. on Uncertainty in Artificial Intelligence, pages 98--103, Cambridge, Mass., July 1990.

....of the network s moral graph. Following Pearl s stochastic simulation algorithms [32] the suitability of Stochastic Local Search (SLS) algorithms for MPE was studied in the context of medical diagnosis applications [33] and more recently in [17] Best First search algorithms were proposed [41] as well as algorithms based on linear programming [37] Various authors have worked on extending some of these algorithms to the task of finding the k most likely explanations [24, 42] 2.6 Bucket and Mini Bucket Elimination Algorithms In this subsection we summarize the main algorithms that ....

....algorithms. It would be interesting to compare our algorithms with search based algorithms for MPE. Search is normally not the method of choice for probabilistic inference. Still some search methods and integer programming approaches have been pursued and it would be good to compare against those [37, 41]. 7 Summary and Conclusion The paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems that are specified by a set of dependencies. The framework can capture many classes of problems, such as those defined on belief networks, influence ....

S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer, Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.

....of the network s moral graph. Following Pearl s stochastic simulation algorithms [29] the suitability of Stochastic Local Search (SLS) algorithms for MPE was studied in the context of medical diagnosis applications [30] and more recently in [17] Best First search algorithms were proposed [39] as well as algorithms based on linear programming [36] Various authors have worked on extending some of these algorithms to the task of finding the k most likely explanations [23, 40] 2.6 Bucket and Mini Bucket Elimination Algorithms In this subsection we summarize the main algorithms that ....

....MPE algorithms. It would be interesting to compare our algorithms with search based algorithms for MPE. Search is normally not the method of choice for probabilistic inference. Still some search methods and integer programming approaches were pursued and it would be good to compare against those [36, 39]. 7 Summary and Conclusion The paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems that are specified by a set of dependencies. The framework can capture many important classes of problems, such as those defined on belief networks, ....

S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.

.... this representation technique and the semantics of uncertain knowledge [12,14,19] In parallel to the progress on the theoretical foundation of knowledge representation, advances have also been made in the algorithmic development of efficient inference schemes for use in a Bayesian belief network [5,11,16,17,21,22]. Recently the feasibility and the utility of applying Bayesian belief network to develop diagnostic systems of various domains have been demonstrated. These encouraging news have resulted in a significant increase in the application of Bayesian belief network modeling across various domains ....

Shimony S.E. and Charniak E., 1990. A New Algorithm for Finding MAP Assignments to Belief Networks, Proc. of the Conf. on Uncertainty in AI, Cambridge, MA, pp. 98-103.

....various approaches, especially in the context of medical diagnosis. Our work on greedy algorithms can be viewed as an extension of the line of work presented in [10] 11] ranging from two layered networks to general belief networks. More recently, best first search algorithms were proposed [17] as well as algorithms based on linear programming [15] Various other authors have worked on extending some of these algorithms to the task of finding the k most likely explanations [7] 18] 3 Competing Algorithms 3.1 Bucket and Mini Bucket Elimination The Bucket Elimination (Elim MPE) is a ....

Shimony, S. E., Charniack, E., 1900. A New Algorithm for Finding MAP Assignments to Belief Networks, In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer (Eds.), Uncertainty in Artificial Intelligence 6, pp. 185-193. Elsevier Science Publishers B. V. (North Holland).

....These methods yield upper and lower bounds on the inference probabilities. Search based algorithms for probabilistic inference include nestor [5] and, more recently, algorithms restricted to two level (bipartite) noisy OR belief networks [16, 28, 29] and other more general algorithms [11, 17, 18, 30, 32, 34]. Approximation algorithms are categorized by the nature of the bounds on the estimates that they produce and by the reliability with which the exact answer lies within these bounds. The following inference problem instance characterizes the two forms of approximation [10] Instance: A real ....

S. E. Shimony and E. Charniak. A new algorithm for finding MAP assignments to belief networks. In Proceedings of Sixth Conference on Uncertainty in Artificial Intelligence, pages 98--103, Cambridge, Massachusetts, 1990.

....minimality, irredundancy, and relevancy. Further research on finding the most probable composite hypotheses should also be exemplified on the algorithms developed by Pearl [5] and Cooper [19] which details were thoroughly discussed in Chapter 8 of [21] and the algorithm by Shimony and Charniak [17]. Pearl s algorithm [5] on finding the most probable composite hypothesis in a singly connected network is based on the propagation of the maximum probability values through a set of causal and diagnostic functions associated with the nodes in a network. The product of these probability values ....

....be applied. One of the limitations of this approach is that the search complexity can grow exponentially with an extra propositional variable added in each level of the incremental search in approaching the desired (local) composite hypotheses. Another approach being taken by Shimony and Charniak [17] is similar to Cooper s in that the MPE is formulated as a search problem, but no restriction is imposed in the probability distributions. The basic idea of Shimony and Charniak is to transform a Bayesian network into a Weighted Boolean Function Directed Acyclic Graph (WBFDAG) which permits the ....

S.E. Shimony and E. Charniak, "A New Algorithm for Finding MAP Assignments to Belief Networks," Proceedings of the Conference on Uncertainty in Artificial Intelligence, Cambridge, MA (1990) pp. 98-103.

.... ) 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 ....

....the task is to identify the most likely input message which was transmitted over a noisy channel, given the observed output. Researchers have investigated various approaches to finding the mpe in a belief network. See, e.g. 35, 9, 36, 37] Recent proposals include best first search algorithms [48] and algorithms based on linear programming [41] The problem is to find x 0 such that P (x 0 ) max x P (x; e) max x Pi i P (x i ; ejx pa i ) where x = x 1 ; xn ) and e is a set of observations, on subsets of the variables. Computing for a given ordering X 1 ; Xn , M = max ....

S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185-- 193, 1991.

.... algorithms for the MPE task [Pearl, 1988] the suitability of Stochastic Local Search (SLS) algorithms for MPE was studied in the context of medical diagnosis applications [Peng and Reggia, 1989] and more recently in [Kask and Dechter, 1999b] Best first search algorithms were also proposed in [Shimony and Charniak, 1991] as well as algorithms based on linear programming [Santos, 1991] 2 Background 2.1 Notation and definitions Belief Networks provide a formalism for reasoning about partial beliefs under conditions of uncertainty. They are defined by a directed acyclic graph over nodes representing random ....

S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.

....1992 ] has a backward chaining search algorithm for incremental term computation , where he has concentrated on saving and not recomputing shared structure in the search. This seems to be a very promising approach for when we do not have as extreme probabilities as we have assumed in this paper. Shimony and Charniak [ 1990 ] have an algorithm that is a backward chaining approach to finding the most likely possible world. The algorithm is not as simple as the one presented here, and has worse asymptotic behaviour (as it is a top down approach see above) It has not been used to find prior or posterior ....

S. E. Shimony and E. Charniak. A new algorithm for finding MAP assignments to belief networks. In Proc. Sixth Conf. on Uncertainty in Artificial Intelligence, pages 98--103, Cambridge, Mass., July 1990.

....our probabilistic estimates, which de Kleer cannot do. One of the features of our work is that finding minimal conflicts is not essential to the correctness of the program, but only to the efficiency. Thus we can explore the idea of saving time by finding useful, but nonminimal conflicts quickly. Shimony and Charniak [1990] , Poole [1992a] and D Ambrosio [1992] have proposed back chaining search algorithms for Bayesian networks. None of these are nearly as efficient as the one presented here. Even if we consider finding the single most normal world, the algorithm here corresponds to forward chaining on definite ....

S. E. Shimony and E. Charniak. A new algorithm for finding MAP assignments to belief networks. In Proc. Sixth Conf. on Uncertainty in Artificial Intelligence, pages 98--103, Cambridge, Mass., July 1990.

....This measure is Pearl s most probable explanation criterion (MPE) In this section, our goal is to apply our linear constraint satisfaction approach to belief revision in Bayesian networks. Although this could be done by first transforming the Bayesian network into a cost based abduction graph [68] and then transforming the graph into a constraint system, a more natural and straightforward method will be given below. See also [54, 57] We will show how to directly transform a Bayesian network into an equivalent constraint system. 4.1.1 Constraints Formulation We first observe that a ....

....the size of the conditional probability tables. For example, consider image processing where each pixel is represented by a r.v. 19] Yet, of the other existing algorithms for performing belief revision, namely Pearl s message passing scheme [41] and Shimony and Charniak s cost based approach [68], message passing is incapable of generating alternative explanations while the cost based method suffers from the heuristic problems outlined in Section 3. Given this dearth of algorithms, we believe ours to be a plausible alternative. Through various tests, we have noticed that our method ....

Solomon E. Shimony and Eugene Charniak. A new algorithm for finding map assignments to belief networks. In Proceedings of the Conference on Uncertainty in Artificial Intelligence, 1990.

....much faster. We investigate this approach for the Most Probable Explanation (MPE) task. It appears in applications such as medical diagnosis, circuit diagnosis, natural language understanding and probabilistic decoding. Some earlier work on MPE can be found in [ Pearl, 1988; Peng and Reggia, 1989; Shimony and Charniak, 1991; Santos, 1991 ] Section 3 presents the relevant algorithms against which we will be comparing. Section 4 describes our branch and bound scheme and its guiding heuristic function. Section 5 presents the empirical evaluations while section 6 provides discussion and conclusions. 2 Notation and ....

S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.

.... Pearl, 1988 ] the suitability of Stochastic Local Search (SLS) algorithms for MPE was studied in the context of Medical diagnosis applications [ Peng and Reggia, 1986 ] Peng and Reggia, 1989 ] and more recently in [ Kask and Dechter, 1999b ] Best first search algorithms were also proposed [ Shimony and Charniak, 1991 ] as well as algorithms based on linear programming [ Santos, 1991 ] 2 Background 2.1 Notation and definitions Belief Networks provide a formalism for reasoning about partial beliefs under conditions of uncertainty. They are defined by a directed acyclic graph over nodes representing random ....

S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.

....These costs can be seen as log probabilities [7] One can view the current work as extending Hobbs et al. s to derive posterior probabilities in a consistent manner. 6. 3 Logic and Bayesian networks The representation of Bayesian networks is related to the work by Charniak and Shimony [7, 63]. Instead of considering abduction, they consider models that consist of an assignment of values to each random variable. The label of [63] plays an analogous role to our hypotheses. They however, do not use their system for computing posterior probabilities. It is also not so obvious how to ....

....in a consistent manner. 6.3 Logic and Bayesian networks The representation of Bayesian networks is related to the work by Charniak and Shimony [7, 63] Instead of considering abduction, they consider models that consist of an assignment of values to each random variable. The label of [63] plays an analogous role to our hypotheses. They however, do not use their system for computing posterior probabilities. It is also not so obvious how to extend their formalism to more powerful logics. Horsch and Poole [22] Breese [5] have defined systems that incorporate Probabilistic Horn ....

S. E. Shimony and E. Charniak. A new algorithm for finding MAP assignments to belief networks. In Proc. Sixth Conf. on Uncertainty in Artificial Intelligence, pages 98--103, Cambridge, Mass., July 1990. Probabilistic Horn abduction and Bayesian networks 61

....state combinations of the original 4. Assuming n states per node, our new node would require n 4 states. Obviously, for large n and large multiply connected subgraphs, our state space explodes combinatorially. For example, consider nodes which may represent map locations. Shimony and Charniak in [24] showed that belief revision can be solved using a best first search strategy. Hence, the problem of network topology is absorbed in the choice of a best first search heuristic. Further 5 In essence, a notion of backtracking is now present in this system. By carefully choosing an alternative ....

Solomon E. Shimony and Eugene Charniak. A new algorithm for finding map assignments to belief networks. In Proceedings of the Conference on Uncertainty in Artificial Intelligence, 1990.

....ALGORITHM FOR MPE Following Pearl s propagation algorithm for singlyconnected networks [ Pear 88 ] researchers have investigated various approaches to finding the MPE in BN. Early attempts are given in [ Coop 84; PeRe 86; PeRe 89 ] Recent proposals include best first search algorithms [ ShCh 91 ] and algorithms based on linear programming [ Sant 91 ] The problem is to maximize the function max x P (x) max x Pi i P (x i jx pa i ) when x = x 1 ; xn ) Consider an arbitrary ordering of the variables (X 1 ; Xn ) Partition the conditional probability matrices fP i g into ....

S.E. Shimony and E. Charniack, "A new algorithm for finding MAP assignments to belief networks,". In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer ed., Uncertainty in Artificial Intelligence 6, pp. 185193, New York, 1991.

....of Medical Diagnosis Network Node names are abbreviated, e.g. lc for Lung cancer . The step numbers in the figure refer to construction steps as defined below. 3.3. 1 Constructing the WAODAG To convert our problem into the WAODAG formulation, we perform a construction similar to [8] or [44]. The algorithm is given a belief network B = V; A; P ) and evidence E . Note that query nodes essentially become evidence nodes, in the context of searching for the best IB assignment. Assume without loss of generality that all nodes are either evidence or query nodes, or ancestors of some ....

Solomon E. Shimony and Eugene Charniak. A new algorithm for finding MAP assignments to belief networks. In Proceedings of the 6th Conference on Uncertainty in AI, pages 98--103, 1990.

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S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.

No context found.

S.E. Shimony and E. Charniack, "A new algorithm for finding MAP assignments to belief networks,". In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer ed., Uncertainty in Artificial Intelligence 6, pp. 185193, New York, 1991.

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S.E. Shimony and E. Charniak. A new algorithm for finding map assignments to belief networks. In P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer Eds. Uncertainty in Artificial Intelligence, volume 6, pages 185--193, 1991.

No context found.

S. E. Shimony and E. Charniak. A new algorithm for finding MAP assignments to belief networks. In Proc. Sixth Conf. on Uncertainty in Artificial Intelligence, pages 98--103, Cambridge, Mass., July 1990.

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S. E. Shimony and E. Charniak. A new algorithm for finding MAP assignments to belief network. In UAI99, 1999.

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