If P( cj | xi ) are already known, where i=1,2,...n; j=1,2,...k;
How do I calculate/estimate:
P( cj | xl , xm , xn ), where j=1,2,...k; l,m,n 
{1,2,...n} ?
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A:
EDIT2 (following the OP's comment)
From bayes rule we know that P(C|x1,x2,x3) ~ P(C)*P(x1,x2,x3|C) and therefore for classification, you compute that expression for all C=j and predict the most likely class (MAP).
Now to compute P(x1,x2,x3|C), for i.i.d observations, this can be written as: P(x1,x2,x3|C) = P(x1|C)*P(x2|C)*P(x3|C), which given a parametric model each could be computed easily.
Amro
2010-04-11 16:42:52
No,seems this is not what I'm doing.`C_i` denotes Categories,while `X_i` denotes samples.So my question is how to classify different samples.
2010-04-12 08:40:32
given what little details you're sharing, no wonder both @aduric and I misunderstood the question!
Amro
2010-04-12 17:15:40
Sorry man,now that you understand what I mean,do you have a solution ?Can I just use **P( c_j | x_l ) * P( c_j | x_m ) * P( c_j | x_n )** to approximate **P( c_j | x_l , x_m , x_n )**
2010-04-13 14:07:19
Seems BNT can also be used to do this job by setting `sizeNodes` to `[2 2 2 2]`?
2010-04-13 14:44:48
no that was a different thing. See my edit above..
Amro
2010-04-13 15:30:04
It seems to me `independent is` enough,why do you require it to be `identically distributed` too?
2010-04-13 15:46:08
This doesn't look like an answer to the question. He didn't ask about Bayes Nets, nor do I think he needs them.
ziggystar
2010-04-14 08:18:29
there was some confusion at first ;)
Amro
2010-04-14 13:57:47
A:
What you want to do is not possible without further information or simplifying assumptions.
The conditional probability P(A|B,C) is not (completely/at all :) determined by P(A|B) and P(A|C).
ziggystar
2010-04-13 17:21:31