Marginalisation Noisy Adder

[joergweber79]

Hello,

suppose to have two connected chance nodes A and B (each with only two variables). Then the probability of node B can be obtained by applying:

P(B)=P(B|A)*P(A)+P(B|not(A))*P(not(A)

But what if chance node B is a Noisy Adder with a LEAK of 0.95. How can the probability of B be computed? (see attached file)

1. Can you please provide some Formula?

2. What is the formula for computing probabilities of A and B, after having entered soft-evidence p=0.1 on node B?

Sincerely,

Joerg

[adam]

Joerg,

You can read more about the noisy-adder in a technical report and my Ph.D. thesis. These are available at:

http://zagorecki.com/web_documents/zago ... verage.pdf
http://zagorecki.com/web_documents/Zagorecki-PhD.pdf (pages 104-114)

What is known in GeNIe as the noisy-adder in the two documents will be refered as the noisy-average. Sorry for this mess.

There is one more difference -- GeNIe has implemented weighting schema that is not discussed in great detail in those documents.

To achieve the effect of non-weighted model discussed in those documents in GeNIe you should use the weight for leak as a very small value (e.g. 0.000000001) and 1 for all other parents I attached here a GeNIe model that implements the example discussed in those documents.

If you want to see a complete CPT defined by the model it is enough to press the Show CPT button in the GeNIe's node definition dialog.

Cheers,
Adam