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Recursive Noisy-OR

Recursive Noisy-OR. Authors : Lemmer and Gossink. Recursive Noisy-Or Model. A technique which allows combinations of dependent causes to be entered and used for estimating the probability of an effect Proposed by Lemmer and Gossink extension of basic Noisy-Or model.

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Recursive Noisy-OR

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  1. Recursive Noisy-OR Authors : Lemmer and Gossink

  2. Recursive Noisy-Or Model • A technique which allows combinations of dependent causes to be entered and used for estimating the probability of an effect • Proposed by Lemmer and Gossink extension of basic Noisy-Or model. • Claim that with this algorithm accurate Bayes models can tractably be built

  3. Continue… • It solves knowledge acquisition as it requires n parameters where n is the number of parent nodes and m parameters where m denotes the synergy/interference of two or more parent nodes on the child node. • Categorization of Dependent and Independent causes

  4. Formula Where: pR(x) conditional probability pE(x) is the conditional probability provided for dependent causes by an expert

  5. Example Let x={a,b,c} be three causes affecting B then if we assume the following values of probabilities provided by expert then: p(a)= 0.5 p(b)=0.6 p(c)=0.7 If the expert tells us that the two causes a and c are causally dependent and provides us with the estimate of that probability then pR (a,c)=0.9 pR (a,b) = 1-(1-p(a)*(1-p(b))) = (1- 0.5*0.4) = 0.8 {a,b are independent}

  6. pR (b,c) = 1-(1-p(b)*(1-p(c))) = (1-0.4*0.3) = 0.88 {b,c are independent} Then to calculate pR(a,b,c) by RNOR model we use the following formula: pR(a,b,c) =1 - [(1- pR(a,b))(1- pR(b,c))(1- pR(a,c))] / [(1- pR(a))* (1- pR(b))*(1- pR(c))] = 0.96

  7. Advantages of RNOR • It preserves Synergy that is the effect of combination of these causes is greater than the combined independent product. • It preserves Interference that is the combination of these causes is less than the combined independent product. • Estimates of probability are appropriate as compared to simple Noisy-Or model Comparative study of Knowledge Elicitation Techniques in Bayesian Networks

  8. Limitations • It cannot handle Inhibition that is when one cause adversely effects the other cause and its combined probability is less than the minimum probability of either of them • Potential problem with RNOR is that its computation can become undefined if denominator is equal to one

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