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 pR(x) conditional probability pE(x) is the conditional probability provided for dependent causes by an expert 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

Comparative study of Knowledge Elicitation Techniques in Bayesian Networks 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

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