Hi, hope someone can comment on my reasoning (due to lack of
confidence in statistics) on this probability problem:
I want to find the joint probability of a hierarchical classifier
system. It consists of 4 individual classifiers C1, C2, C3 and C4:
C1
|
---------
| | |
C2 C3 C4
C1 classifies between groups {a,b},{c,d,e} and {f,g}
C2 classifies between a and b
C3 classifies between c, d and e
C4 classifies between f and g
So, in order to classify an item (e.g. f) correctly it is required
that C1 classifies correcly such that the next classifier to be
invoked is C4 (that classifies between f and g).
I have the individual classification rates and the confusion matrices
for each classifier - but I am not sure how to compute the "joint"
probability..
The individual classification rates are as follows:
C1: classification rate: 99.36%
Confusion matrix:
400 0 0
0 596 4
0 5 395
(as you see there are 400 of type {a,b}, 600 of {c,d,e} and 400 of
{f,g}.)
C2: classification rate: 100%
C3: classification rate: 99.33%
C4: classification rate: 86.0%
Can I simply calculate the joint probability as:
P = (400*0.9936*1.0 + 596*0.9936*0.9933 + 395*0.9936*0.86 ) /
(400+596+395)
P = 95.12
???
I would appreciate any comments on the correctness of this :)
Many Thanks
McIlfar
.
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