Is it possible to model using Bayesian Network (probabilistic graphical model) if you have no idea at all of the interaction of the variables in the data? From my reading, I find that Bayesian network is very intuitive and aligns well with human reasoning. As such, I think that it should have a high performance. However, if one has no knowledge of the dataset, say a dataset for a hospital patients, how can one decide on the interaction between the nodes in the network? Or is this a big flaw of BN?
In the question title, you said "no prior knowledge of the data". What does this mean exactly? Does it mean:
you do not have the prior data, or
you have the prior data but you don't have any knowledge on the relationships the parameters in the data have.
As for Bayes, you need both the prior data and prior knowledge. Note that you may be able to find the prior knowledge from the prior data (e.g. using some machine learning tools). The prior knowledge is the set of probabilities used in Bayes. Based on this prior data and prior knowledge, you build a Bayes model. Now, when you have new data (from the same population), you can pass it through the built Bayes model and make predictions on the new data.
This link may help: Link (I haven't read the whole page; I just googled it and found that there's also some information regarding Bayes and patients.)
Hope this helps.
There are ways of learning the structure of a Bayesian network from the data. So the answer to your question is positive.
I’m reading Judea Pearl’s Book: Probabilistic Reasoning in intelligent systems; I haven’t reach the chapter where he explains the methods for what you are asking but I know there is a chapter about that. The chapter is: Ch. 8 - Learning Structure From Data
Courseras’s course on probabilistic graphical models by Daphne Koller also has a lesson on that. She also has a book on the topic which is more recent than Judea’s and also includes a chapter that may be what you are asking for: Ch. 18 - Structure Learning in Bayesian Networks