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mark
Posts: 179
Joined: Tue Nov 27, 2007 4:02 pm

Post by mark »

Almost. This is the correct formula, P(d1|b1&c1) = C(d1,b1,c1) / C(b1,c1), where you should note that I changed the probabilities to counts. So you don't have to divide by the total number of data.
megha
Posts: 23
Joined: Mon Mar 03, 2008 11:43 am

Post by megha »

ok and when any particular combination of states of parent and child occurs '0' times then it gives conditional probability of child as '0' and in case if any particular combination of parents states appear '0' times then then the value of conditional probability of child will be 'infinity' and according to you EM algorithm should be used to handle this situation? also in case if the table is not having missing data, but just particular combinations are not present in table, b'coz what i've seen in GeNIe is if any particular combination of parents states is appearing '0' times then for different states of child with that combination of parents ,equal probabilities have been assigned.
mark
Posts: 179
Joined: Tue Nov 27, 2007 4:02 pm

Post by mark »

If a combination of parents does not occur, EM will leave the original (or randomized) values in the CPT. Note that if you do structure learning, EM is not automatically invoked so you'll have to do that manually.
megha
Posts: 23
Joined: Mon Mar 03, 2008 11:43 am

Post by megha »

Hi,
Can anyone tell me please, have you used any correction while calculating conditional probability table, when the parentchild states combination or parent states combination appears zero times in the table?
mark
Posts: 179
Joined: Tue Nov 27, 2007 4:02 pm

Post by mark »

There is no correction and the original CPT values will not be changed, unless you invoke EM with randomization. In that case the CPT values are simply random values.
megha
Posts: 23
Joined: Mon Mar 03, 2008 11:43 am

Post by megha »

Actually, Mark the same confusion again, before applying EM when the probabilities are assigned to states, there are some parent states combination which appears 0 times in data, but still there are probabilities assigned to those states. similarly some parentchild combination also appears 0 times in data then the probabilities for them must be 0 but this is not the case in GeNIe, those states are assigned with probabilities,remember i'm talking this before applying EM.
mark
Posts: 179
Joined: Tue Nov 27, 2007 4:02 pm

Post by mark »

Like I said before, I don't actually know how those parameters are estimated at the moment, but apparently it is incorrect. We are reimplementing Greedy Thick Thinning and the new version will invoke EM or return uniform distributions after the structure has been learned.
megha
Posts: 23
Joined: Mon Mar 03, 2008 11:43 am

Post by megha »

Hi,
while learning the CPTs for each node have u also calculated the marginal probability for each state of that node? b'coz these probabilities will be needed to calculate the inferences after setting the evidence, by using bayes theorem?
mark
Posts: 179
Joined: Tue Nov 27, 2007 4:02 pm

Post by mark »

Marginal probabilities are calculated after setting evidence in the network, and not before. So learning just learns CPTs and nothing more.
megha
Posts: 23
Joined: Mon Mar 03, 2008 11:43 am

Post by megha »

Hello Mark,
As I've asked u earlier regarding the zero probabilities(i.e. wht if certain parents states combination is appearing 0 times) and how genie handled that situation, I think in that case laplace correction must have been applied, right? b'coz in that case only it gives those probability calculations.
mark
Posts: 179
Joined: Tue Nov 27, 2007 4:02 pm

Post by mark »

Doesn't the Laplace correction change a probability distribution to a more uniform one? That would mean we should see no 0/1 probabilities in the CPTs, but we do, so I doubt if the Laplace correction is used.
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