Learning Parameter algorithm

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heyifan
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Joined: Tue Aug 25, 2020 2:05 pm

Learning Parameter algorithm

Post by heyifan »

I have constructed the structure of BN and have a dataset to learn the CPT. The dataset contains 90 records with states of 9 binary variables. The problem is that one of the nine varibles has only one state in all records. Will the parameter learning result still be valid? Thanks a lot if someone could help me with that question.
marek [BayesFusion]
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Joined: Tue Dec 11, 2007 4:24 pm

Re: Learning Parameter algorithm

Post by marek [BayesFusion] »

The results should be valid, although a variable with just one state is just a constant, which carries no information. Constants are not allowed in structure learning but they will be accepted in parameter learning. The result of learning will be a large probability for the state represented in the data and some small probabilities for the other states.
I hope this helps,

Marek
heyifan
Posts: 7
Joined: Tue Aug 25, 2020 2:05 pm

Re: Learning Parameter algorithm

Post by heyifan »

Thanks! If I delete the node which only has one state, the CPT of other nodes learning by dataset won't be affected, right?
marek [BayesFusion]
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Posts: 430
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Re: Learning Parameter algorithm

Post by marek [BayesFusion] »

It depends what you mean by "delete." If you just delete a node, the CPTs of its child nodes will be quite strongly affected -- they will shrink by one dimension. If you mean not taking this node in consideration when learning, then it depends what the other graph connections are. If you mean "marginalizing," which also results in deleting the node, then the other nodes are not going to be affected in terms of their marginal probability distributions.

I hope this helps. If not, please clarify your question.
Cheers,

Marek
heyifan
Posts: 7
Joined: Tue Aug 25, 2020 2:05 pm

Re: Learning Parameter algorithm

Post by heyifan »

marek [BayesFusion] wrote: Tue Apr 13, 2021 1:20 pm The results should be valid, although a variable with just one state is just a constant, which carries no information. Constants are not allowed in structure learning but they will be accepted in parameter learning. The result of learning will be a large probability for the state represented in the data and some small probabilities for the other states.
I hope this helps,

Marek
why the result of learning will be a large probability not 100%? how to explain the learning result? Thanks a lot if you could help.
marek [BayesFusion]
Site Admin
Posts: 430
Joined: Tue Dec 11, 2007 4:24 pm

Re: Learning Parameter algorithm

Post by marek [BayesFusion] »

Neither GeNIe nor SMILE will allow you to create discrete chance nodes with just one state, i.e., constants. So, you cannot have a node with just one state. The EM algorithm tries to avoid zeros in the CPTs, so the one state that you have in your data would have a very large probability and the other state(s) of the node corresponding to that constant column would have some small fractions.

I hope this helps,

Marek
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