For an university assignment I have to use the HuginLite software to do some probabilistic inferences with different algorithms. One of these algorithms is Naive Bayes but its graph is not built automatically by the software, so I have to construct it and create the conditional probability table.
The scenario is the one of 4-5 genes expression related to Acute Myeloid Leukemia (AML) which is the target of the model. I've understood that in Naive Bayes every feature is considered conditionally independent from others, so I've supposed that in the graph they are non connected by an edge, so I've thought that the graph was a simple connection of each genes to the AML node like in the image below.
This seems to be wrong, so basically there is something that I'm missing or I've not understood well on how to build the graph given data.
The data set is structured with entries of yes/no values for genes and disease expression, like this (is just a portion of the dataset):
ATP2B4,NAP1L1,MDK,PCCB,MDS1,AML no,no,no,yes,yes,no no,yes,yes,yes,yes,no no,yes,no,yes,no,no no,no,yes,yes,yes,no no,no,no,yes,yes,no no,no,no,yes,yes,yes
I've computed the probability of expression of each gene simply counting every 'yes' occurrence and divided for the number of entries, the same for conditional probabilities like P(ATP2B4 | AML) counting occurrences with ATP2B4 = 'yes' and AML = 'yes'. In order to fill the CPT for AML I've used the Bayes theorem and multiplied every conditional probabilty for every possible configuration.
It has been told to me that the graph itself is wrong and so even the CPT. How do I build that graph given a dataset of occurences? I'm struggling on this problem since some days.