Building blocks of GeNIe > Components of GeNIe models

Canonical probabilistic nodes, such as Noisy-MAX/OR, Noisy-MIN/AND and Noisy-Adder gates, implemented by GeNIe, are convenient knowledge engineering tools widely used in practical applications. In case of a general Chance binary node with n binary parents, the user has to specify 2n parameters, a number that is exponential in the number of parents. This number can quickly become prohibitive - please note that when the number of parents n is equal to 10, we need 1,024 parameters, when it is equal to 20, the number of parameters is equal to 1,048,576, with each additional parent doubling it. A Noisy-OR model allow for specifying this interaction with only n+1 parameters, one for each parent plus one more number. This comes down to 11 and 21 for n equal to 10 and 20 respectively.

The savings stemming from the use of canonical models in terms of the number of probability elicitations may be dramatic, especially when the number of parents of a node becomes large. Canonical models are not only great tools for knowledge engineering - they also lead to significant reduction in computation through the independences that they model implicitly. Using canonical gates makes thus model construction easier but also leads to models that are easier to solve.

This section gives a brief introduction to how GeNIe implements Noisy-OR/MAX, Noisy-AND/MIN and Noisy-Average gates, assuming that the reader is familiar with the concepts and has a basic knowledge of the principles applied in these gates. To learn more about the Noisy-OR/MAX and Noisy-AND/MIN gates and their practical value, please refer to the excellent paper on the topic by Henrion (1989). Diez & Druzdzel (2006) summarize the theory behind the Noisy-MAX and other canonical gates.