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MASS
MCAL
Noisy CPT I 1
I 1
Noisy CPT I 2
I 2
MASS
MCAL
false
true
false
true
I 1
I 2
false
1
0
false
1
0
true
0.15
0.85
true
0.4
0.6
BC
BC
I 1
I 2
false
true
false
false
1
0
false
true
0
1
true
false
0
1
true
true
0
1
Fig. 9. Example of a noisy-OR model for breast cancer prediction
patient having breast cancer (BC), the so-called effect variable. It is also known
that masses are more frequent occurring sign, which is reflected in the noisy
probability distributions P ( I 1 |
MCAL). Finally, the domain
knowledge suggests that the combined occurrence of both signs increases the
probability for having breast cancer, which is modelled by the logical OR as an
interaction function f ( I 1 ,I 2 ) for the effect BC.
Then the probability of having breast cancer given the states of MASS and
MCAL is computed as follows:
MASS) and P ( I 2 |
P (BC = true
|
MASS , MCAL) =
=
P (BC = true
|
I 1 ,I 2 ) P ( I 1 |
MASS) P ( I 2 |
MCAL)
f ( I 1 ,I 2 )= true
= P ( I 1 = true
|
MASS) P ( I 2 = true
|
MCAL) +
P ( I 1 = true
|
MASS) P ( I 2 = false
|
MCAL) +
P ( I 1 = false
|
MASS) P ( I 2 = true
|
MCAL) .
For example, given the evidence of MASS = true and MCAL = false then
the probability for breast cancer is:
P (BC = true
|
MASS , MCAL) = 0 . 85
·
0+0 . 85
·
1+0 . 15
·
0=0 . 85 .
Now suppose that MASS = true and MCAL = true . Then we obtain
P (BC = true
|
MASS , MCAL) = 0 . 85
·
0 . 6+0 . 85
·
0 . 4+0 . 15
·
0 . 6=0 . 94 ,
 
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