PRIOR LINK PROBABILITY parameter of the Bayesian Search algorithm

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c.martinez
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Joined: Thu Feb 17, 2022 11:08 am

PRIOR LINK PROBABILITY parameter of the Bayesian Search algorithm

Post by c.martinez »

Hello,

I had a question about the Bayesian Search algorithm.

I need to build a Bayesian network from a small database for a project. My database has about 82 records and it is not possible to extend it.

Since the database is small, the GENIE algorithm does not establish many probabilistic relationships between the nodes (I have 23 nodes).

The rest of the algorithms I should not use because my database does not meet the requirements, for example, to come from a normal distribution in the case of the PC algorithm or to be independent variables to be able to use one of the Naive Bayes algorithms. Therefore, the one that best fits my database is the Bayesian Search algorithm. The Greedy Thick Thinning algorithm gives me the same result as Bayesian Network algorithm.

I have tried to touch some parameters of bayesian search and I have seen that when I modify the parameter "PRIOR LINK PROBABILITY" and I give it a value of 0.9 instead of leaving its default value of 0.01, it finds me several probabilistic relationships to work on.

My question is whether modifying that parameter and setting it to 0.9 is wrong or trivial. I don't quite understand what this parameter refers to and I would like to know if the network I get could be considered as valid (after the validation process of the links between nodes and the sensitivity analysis) or on the contrary, changing this parameter of the algorithm the process is wrong.

Thanks in advance
Regards
marek [BayesFusion]
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Posts: 430
Joined: Tue Dec 11, 2007 4:24 pm

Re: PRIOR LINK PROBABILITY parameter of the Bayesian Search algorithm

Post by marek [BayesFusion] »

Hi,

The "prior link probability" parameter influences the likelihood of the Bayesian Search algorithm producing arcs, as higher values favor arcs. So, it is not really surprising that when you increased its value, you got a denser network. My answer to the question whether you can modify the value of this parameter is that you should increase it if you tend to get sparse networks and you do when the number of data records is very small, like in your case. While the structure learned from a small data set will remain unreliable, you may get some connections with the parameter being higher. The proof is in the pudding, however, so I would suggest validating your models in how well it predicts what you want to predict. If your denser model produces more accurate estimates, it was justified to use a higher value of the "prior link probability".

I would not dismiss the Naïve Bayes, TAN and ABN algorithms -- while they will not give you much information in terms of the causal structure among your variables, they may produce more accurate models with such a small data set. It is worth trying. Validation should be your guide.

I hope this helps,

Marek
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