Glenn Shafer, Prakash P. Shenoy, and Khaled Mellouli. Propagating belief functions in qualitative Markov trees. International Journal of Approximate Reasoning, 1(4):349--400, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....differences. 1 Introduction Expensive computational cost of Dempster s rule in DS theory led to a stream of study on efficient implementations of the rule over the last two decades. The proposed approaches have emphasized either exact implementations of the rule (e.g. 1] 6] 10] [11], 13] 17] etc. or its approximations (e.g. 2] 3] 4] 15] 16] etc. under the assumption that evidence distributions follow certain structures. Among all these approaches, the method on belief propagation in qualitative Markov trees has been popular. As proved in [11] with this ....

....[6] 10] 11] 13] 17] etc. or its approximations (e.g. 2] 3] 4] 15] 16] etc. under the assumption that evidence distributions follow certain structures. Among all these approaches, the method on belief propagation in qualitative Markov trees has been popular. As proved in [11], with this method, the exponential computational complexity in the size of total variables is reduced to the size of the largest node in a tree, a node with the largest number of variables. The major technique supporting the method is local computation [14] which was initiated for propagating ....

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Shafer, G., Shenoy, P. and Mellouli, K.: Propagating belief functions in qualitative Markov trees. Int. J. of Approx. Reasoning. Vol. 1, 1987, 349-400

....sequence prediction methods, a highly parameterized prediction system was implemented. We use a data structure that works for the more complex algorithms, and just ignore some aspects of it for the simpler ones. Figure 4.1: A sample node in a Markov tree. In particular, we build a Markov tree [SSM87, LS94, FX00] in which the transitions from the root node to its children represent the probabilities in a zero th order Markov model, the transitions to their children correspond to a first order model, and so on. The tree itself thus stores sequences in the form of a trie a data ....

Glenn Shafer, Prakash P. Shenoy, and Khaled Mellouli. Propagating belief functions in qualitative Markov trees. International Journal of Approximate Reasoning, 1(4):349--400, 1987.

....the classical independence of frames as Boolean sub algebras and the external independence of frames as elements of a locally nite Birkho lattice, eventually pre guring a solution to the con ict problem based on a pseudo Gram Schmidt algorithm. Not much work has been done along this path; in [9] can be found an analysis of the collections of partitions of a given frame in the context of the hierarchical representation of belief. A wider exposition of the algebraic properties of the families of frames can instead be found in [6] where Chapter 7 is devoted to their lattice theoretical ....

Glenn Shafer, Prakash P. Shenoy, and K. Mellouli, Propagating belief functions in qualitative markov trees, International Journal of Approximate Reasoning 1 (1987), (4), 349-400.

....collection consisted of 2500 documents randomly selected from the journal Computer Science VINITI (journal of abstracts) 1982 1987. In the experiment, 20 queries were used for training and 15 queries were used for 25 testing. MIR systems using the neural network and the Dempster Shafer s model [54, 55] were compared based on their performance on choosing among two query reformulation algorithms for relevance feedback. The results showed that the neural network performed better than the Dempster Shafer s model. Lewis et al. 33] studied the Adaline (see section 2.5.3) as the classifier model ....

G. Shafer, P. P. Shenoy, and K. Mellouli, "Propagating belief functions in qualitative markov trees," International Journal of Approximate Reasoning, vol. 1, pp. 349--400, 1987.

....provided one takes the non distinctness into account in the appropriate way. One particularly attractive way of doing this is suggested by Xu and Smets [112] who introduce an approach which has much in common with Bayesian networks. Methods based on the ShenoyShafer hypertree computation approach [81] can also be used to deal with the problem. 6 Conclusions This article has described an application of belief functions to forecasting demand for a new telecommunications service, Global Mobile Satellite Services. Although the model presented here has been simpli ed, and disguised rather than ....

G. Shafer, P. P. Shenoy, and K. Mellouli. Propagating belief functions in qualitative Markov trees. International Journal of Approximate Reasoning, 1:349-400, 1987.

.... # k=1 # k # j#J k s jk (2) where each s jk is x j or (1 x j ) An edge connects x i and x j in the dependency graph for the problem if x i and x j occur in the same term of (2) Methods that are essentially nonserial dynamic programming have also surfaced in the analysis of Markov trees [135, 136], facility location [31] and Bayesian networks [105] A graph with induced width k is a partial k tree, studied in [4, 5] and elsewhere. 2.1.2 Continuous Relaxations A second contribution of Boolean research was to provide early examples of continuous relaxations for a logical conditions. ....

Shafer, G., P. P. Shenoy, and K. Mellouli, Propagating belief functions in qualitative Markov trees, International Journal of Approximate Reasoning 1 (1987): 349-400.

....evidence correspond to data and domain knowledge respectively, this is a significant restriction. A generalization of the algorithm by Shafer and Logan that manages to take domain knowledge into account is the method for belief propagation in qualitative Markov trees by Shafer, Shenoy and Mellouli [13]. In a qualitative Markov tree the children are qualitatively conditionally independent [14] given the parent, i.e. in determining which element of a child is true, there is no additional information in knowing which element of another child is true once we know which element of the parent is ....

....the second vertex respectively. Because the supported subsets in the hierarchical network of our problem are not disjoint, we can not prune our network to a tree and use the scheme suggested by Gordon and Shortliffe. The two other papers by Shafer and Logan [12] and Shafer, Shenoy and Mellouli [13] concern the case of belief propagation in qualitative Markov trees only. Thus, the methods presented in these three papers are not applicable in the case with evidences in a non prunable network of subsets. Instead of propagating the belief in a hierarchical structure of subsets our algorithm ....

Shafer, G., Shenoy, P. P., and Mellouli, K., Propagating belief functions in qualitative Markov trees, Int. J. Approx. Reasoning 1(4), 349-400, 1987.

....(F1 F4) At this point, KR mod communicates the name of the asked formula to HBS, which requires a belief value for it to UR mod. This value is not available, but UR mod has enough information to compute it. If we imagine that our UR mod consists of a network based implementation of DS theory (Shafer et al., 1987), then the inferences above may be codified by the belief network on the right, where ovals represent variables, and hexagons represent relations among variables (i.e. basic probability assignments defined over the product space of the involved variables) F1 F2 F3 F4 F5 In our case, all the ....

Shafer, G., Shenoy, P.P. and Mellouli, K. (1987) "Propagating Belief Functions in Qualitative Markov Trees", International Journal of Approximate Reasoning 1: 349-400.

....but that book is apparently not yet published. 1. 6 Networks of Non probabilistic representations of Uncertainty (These involve mostly generalizations of point probability) Qualitative Networks: Wel90a] Wel90b] Wel90c] PM93] Par95] Belief Functions: Dem90] Kon86] Mel87] SS86] SSM87] SS90] Wil90] Xu91] ZHS88] WD94b] SSS95] Sri95] Convex Probabilities: BF91] CDM91] CMVL93] CDM93] FB93] Tes92] dCM95] Chr96] Previsions: Gol90] Second Order Distributions: Mus93] NK91] Generalized Axiomatizations: These generalize most of the above types of ....

Glenn Shafer, Prakash P. Shenoy, and Khaled Mellouli. Propagating belief functions in qualitative Markov trees. International Journal of Approximate Reasoning, 1:349--400, 1987.

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Shafer, G., P.P. Shenoy, and K. Mellouli. "Propagating Belief Functions in Qualitative Markov Trees." International Journal of Approximate Reasoning, 1987, 349-400.

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G. Shafer, P.P. Shenoy, and K. Mellouli, Propagating Belief Functions in Qualitative Markov Trees, International Journal of Approximate Reasoning, 1(4), 349- 400, 1987.

.... conditional independence, but also by embedded multi valued dependency models in relational databases [8] by conditional independence in Spohn s theory of ordinal conditional functions [11] 4] by qualitative conditional independence in Dempster Shafer theory of belief functions partitions [9], and by conditional independence in valuation based systems (VBS) 10] capable of representing many di#erent uncertainty calculi. The aim of this paper is to propose the new definitions of conditional independence when uncertainty is expressed under the form of belief functions and then to ....

G. Shafer, P.P. Shenoy, and K. Mellouli, Propagating Belief Functions in Qualitative Markov Trees, International Journal of Approximate Reasoning, 1(4), 349- 400, 1987.

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Shafer, G ., P.P. Shenoy, and K. Mellou li. "Propagating Belief Functions in Qualitative Markov Trees." International Journal of Approximate R easoning, 1987, 349-400.

....As in the case of probability theory, we can avoid the normalization operation in Dempster s rule and do it just once at the very end. n The use of belief functions in expert systems has been widely studied. Some of the influential works in this area are [Shenoy and Shafer 1986, Kong 1986, Shafer, Shenoy and Mellouli 1987, Table 4. The bpa potentials 1 , 2 , 3 , and 4 in Example 6. 2 W R, P 1 2 W R 3 (r, p) r, p) r, p) 90 r .999 (r, p) r, p) r, p) r, p) 10 r, r .001 2 W Q, P 2 2 W Q 4 (q, p) q, p) q, p) 99 q .999 (q, p) q, p) q, p) q, ....

Shafer, G., P. P. Shenoy, and K. Mellouli (1987), "Propagating belief functions in qualitative Markov trees," International Journal of Approximate Reasoning, 1(4), 349--400.

No context found.

Glenn Shafer, Prakash P. Shenoy, and Khaled Mellouli. Propagating belief functions in qualitative Markov trees. International Journal of Approximate Reasoning, 1(4):349--400, 1987.

No context found.

G. Shafer, P.P. Shenoy, and K. Mellouli. Propagating belief functions in qualitative markov trees. International Journal of Approximate Reasoning, 1:349--400, 1987.

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G. Shafer, P. Shenoy and K. Mellouli, "Propagating Belief Functions in Qualitative Markov Trees", Int. J. of Approx. Reasoning, Vol.1, 1987, 349-400.

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Shafer, G., Shenoy, P. P., and Mellouli, K. "Propagating belief functions in qualitative Markov trees", International Journal of Approximate Reasoning, 1 (1987) 349--400.

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