Noisy-Or Classifier

Learning from the training data - I
Let D = {e 1 , . . . , e n } be the training data, where the instances are
e i = {c i , a i } = {c i , a i 1 , . . . , ai k
}, for i=1,. . . ,n.
and n(c, a) is the occurrence of (c, a) in D.
The learning process aims at a model P M maximizing the ability to
correctly predict class C. Assuming i.i.d. data D
CLL(P M | D) =
=
n
∑ log P M (C = c i | A = a i )
i=1
= ∑
a
∑
c
n(c, a) · log P M (C = c | A = a)
= n · ∑
a
P D (A = a) · ∑
c
P D (C = c | A = a) · log P M (C = c | A = a) .