Information Technology Reference
In-Depth Information
p(F
j
|
C
i
) p(C
i
)
P(C
i
|
F
j
)
=−−−−−−−−−−−−−−−−−
p(F
j
)
where
n
=
p(F
j
|
p(F
j
)
C
i
) P(C
i
)
i
=
1
C
i
is concept i
F
j
is feature j
C
i
|F
j
is concept i given feature j
F
j
|C
i
is feature j given concept i
p() is an
a priori
probability function
P() is an
a posteriori
probability function
Once training is done, we should have two stabilize tables to be used to guide
retroduction to
select a concept
from which a
hypothesis
can be constructed.
Each feature, F
j
, in the list provided by a window w
x
will be used to calculate
an
a posteriori
probability of the concept,
Ci
, using the Bayesian rule. The
a priori
probabilities
p(F
j
|C
i
) and p(C
i
) are obtained from the probability density-table given
by the initial training (Table
12.2
). The calculated
a posteriori probabilities
, P(C|F),
are used to calculate ranking weight, R
i
, for every concept C
i
using
R
i
=
|
FL
|
logP( FL
j
C
j
)logP(C
i
)
j=1
where FL is the feature-list and |FL| is the cardinality of the list, i.e. how many
features are in the list.
This ranking function R
i
is actually a variation of Shannon's entropy (Information
Theory). The concepts are ranked according to their relative entropy. The concept
C
i
with the highest relative entropy value with respect to the range of features FL
j
will be the most likely candidate to produce a correct hypothesis. The reason for
this is that the features that contain the most information about the link between an
observed sequence and the associated concept, are those that change the most with
a change of concept. If it fails, the next highest ranking will be used.
12.2.1
The Deductive Process
The deductive process begins with an abduced hypothesis and prepares it for inductive
testing. The deductive process draws consequences from the abduced function (i.e.
prediction, size of representation, etc.) in preparation for the inductive testing. All this
information is packaged and passed on as a frame. A frame is a set of predefined infor-
mation requests that provide the information to fill the fields in a pre-set empty form.
