Bernal S D_2010.pdf - University of Plymouth

.1.3. DEFI^anON AND MATHFMATICAL FORMULATION
For the example described in the Section 3,3.2. if we assume paahi^ - 0'8 and pMnon = 0.7, the
CPT value for Waves=l in the case when both causes are irue can be obtained as follows.
P(W = 1 |g - 1. m - 1 ) - I - (1 - PGales) * (1 " PMocn) - 1 " 0.2 • 0.3 = 0.94
which yields a value consistent with the value that was intuitively generated for the CPT of
the original example. This serves lo illustrate the concept behind the Noisy-OR gate, although
obviously in Ibis case il does not make sense lo use ihe method as the number of parent nodes
and stales is very small.
The Noisy-OR method was originally d&scribed for binary variables (Pearl 1988), although
it was later extended to variables with multiple stales {Srinivas 1993, Diez 1993). However,
the main limitation of this method is thai it requires graded variables to work (Diez 1993),
variables who,se slates can be ordered from lower to higher. The speed of the wind is an example
of a graded variable. However, a variable whose slates are differenl object categories is not.
The model has also been extended to include different weights for each of the parent links
(Kokkonen et al. 2005), such that the relative contribution of each of them can be mi)dulated
according to some learned or hardwired crileria.
Tlie Noisy-OR model describes how causes interact disjunctively. Other canonical models de­
scribe different types of parental interaction, such as the Noisy-AND model which describes
the conjunctive interaction of causes. For more details on ihe Noisy-OR and other canonical
models see Peari (1988) and Die/ (1993).
3.3.4.2 Weighted sum based on compatible parental configurations
An alternative method lo the Noisy-OR is that proposed by Das (2004), based on the concept
of compaiible parental amfigurations. The rationale behind it is to facilitate the acquisiiion of
probabilistic knowledge, when this is obtained from human experts, by reducing the number
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