Bernal S D_2010.pdf - University of Plymouth

3.3. DEFINITION AND MATHEMATICAl. FORMULATION
Therefore the link is defined using ft;;, +ki;^ + ... + kn^ probabilily distributions over X for
Ihe different conipaiible parental confignraiinn. Note Ihese grow linearly with the number of
parents. Given a set of weights W|,...,ii'^', which quantify the relative strength of the parent
nodes' inlluence on ihe child node, the entries of the CPT can be generated using the following
weighted sum expression,
P{X\UU...,UN)= Y. ^'rP{x\(Comp(Vi = Ui)}) (3.34)
i=\..N
It is important to stress thai {Coinp{U, = «,)} is a parental conliguration in the menial model
of the expert where he has chosen to focus on the slate M; of parent (/,, while the rest of the
states of the parents are perceived in his judgement to be in compalible stales with ii,. This
helps ihe expert to simplify his mental model in order lo judge the possible cflect. It does not
mean ihat compalible parental configurations are the only ones lo be found in reality, bul these
are assumed to be more common or normal.
The method described here proposes combining the probability distributions of X given com­
patible parental conligurations, to calculate the states of X given invompanbU: or less common,
parental configurations, by using the weighted sum expression in Hquaiion (3.34). This can
be understood as a kind of interpolation mechanism Ihat exploits the known dala points. Das
(2004) makes use of information geometry to demonstrate how these weighted sums capture
Ihe expert.s' judgemental strategy. The method is being employed to design strategic military
applications for the Australian Deparlmenl of Defence.
Although the method was derived for populating CFTs using human experts, theoretically il
can be extended to systems that obtain their information using training dala with supervised
learning methods. One such domain is hierarchical object recognition, where, due to the greal
ovedap between receptive fields, parent nodes show contextual inlerdependency and can there­
fore exploit this technique. This is discussed further in Chapter f>. where a toy example is used
to illusiraie the concept.
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