Dear friend
Recently, I get confused about the Directed Arc, which represent the causal relationship of the notes, in some Bayesian graph. For example. The directed arc should be from cause to the effect. For example, the FLU, RABIES, EARINF, BRONCH can lead to a FEVER.
But I find in many Bayesian graph, the directed arc is from effect to cause. Like a very typical case: “play tennis”. For the day <sunny, cool, high, strong>, what’s the play prediction?
Apparently, according to the experience, the "wind", "humidity", "temperature" and "outlook" are the causes to decide whether to play tennis, so the directed arcs should be from “wind”, “humidity”, “temperature” and “outlook” to “play tennis”
Question 1: Many references establish the Bayesian net like the following figure, the directed arcs are from “play tennis” to the “wind”, “humidity”, “temperature” and “outlook”. That make me confused, I don’t know the reason.
I want to know whether the directed arc has different meaning in bayesian classifier and bayesian Networks. In bayesian classifier, the directed arc is from "class" to "attributes", But in bayesian Networks, the directed arc is from "cause" to "effect".
The differences of the bayesian classifier and bayesian networks
The differences of the bayesian classifier and bayesian networks
Last edited by wxk8000 on Tue Apr 17, 2018 1:59 pm, edited 4 times in total.

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 Posts: 270
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Re: The question of the arc's direction and the learned network is inconsistent with the experience and book knowledge.
I'm afraid to answer your questions would require me to write a book, or at least a book chapter, on Bayesian network modeling :). May I suggest that you read through a good textbook? We list several good books on our web site (https://www.bayesfusion.com/books).
To give you brief answers, while Bayesian networks are capable of representing causation, modelers can choose the direction of arcs and there is no way of enforcing causal direction of arcs in the formalism.
The two GeNIe model screenshots that you present represent two completely different joint probability distributions and, hence, I am not surprised at all that they give you different results.
You can easily check accuracy of a learned network in GeNIe (look at the chapter on validation in GeNIe manual). As far as the direction of arcs goes, if you are certain about them, you can enter them among the pieces of prior knowledge when performing structure learning (this is also described in detail in GeNIe manual).
I'm sorry to hear that you are confused. I realize that this stuff is not easy, so please be patient and keep reading  I have no doubts that you will master this material some day.
I hope this helps,
Marek
To give you brief answers, while Bayesian networks are capable of representing causation, modelers can choose the direction of arcs and there is no way of enforcing causal direction of arcs in the formalism.
The two GeNIe model screenshots that you present represent two completely different joint probability distributions and, hence, I am not surprised at all that they give you different results.
You can easily check accuracy of a learned network in GeNIe (look at the chapter on validation in GeNIe manual). As far as the direction of arcs goes, if you are certain about them, you can enter them among the pieces of prior knowledge when performing structure learning (this is also described in detail in GeNIe manual).
I'm sorry to hear that you are confused. I realize that this stuff is not easy, so please be patient and keep reading  I have no doubts that you will master this material some day.
I hope this helps,
Marek
Re: The question of the arc's direction and the learned network is inconsistent with the experience and book knowledge.
marek [BayesFusion] wrote:I'm afraid to answer your questions would require me to write a book, or at least a book chapter, on Bayesian network modeling :). May I suggest that you read through a good textbook? We list several good books on our web site (https://www.bayesfusion.com/books).
To give you brief answers, while Bayesian networks are capable of representing causation, modelers can choose the direction of arcs and there is no way of enforcing causal direction of arcs in the formalism.
The two GeNIe model screenshots that you present represent two completely different joint probability distributions and, hence, I am not surprised at all that they give you different results.
You can easily check accuracy of a learned network in GeNIe (look at the chapter on validation in GeNIe manual). As far as the direction of arcs goes, if you are certain about them, you can enter them among the pieces of prior knowledge when performing structure learning (this is also described in detail in GeNIe manual).
I'm sorry to hear that you are confused. I realize that this stuff is not easy, so please be patient and keep reading  I have no doubts that you will master this material some day.
I hope this helps,
Marek
Dear Marek
Recently, I looked some references, I found that there are two different concepts of bayesian. One is the bayesian classifier, the other is the bayesian Network. They are different. Bayesian classifier graph shows the relation of "class" and "attributes", The arc's direction is from the "class" to "attributes", is irrelevant to the causal relations. But in the TAN classifier graph, the arcs between the "attributes" still has the causal relations.
To the Bayesian Networks, the graph can represents the causal Relations between the variables.
I don't know whether my comprehension is appropriate, I need your confirmation and Supplement, thank you!

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 Posts: 270
 Joined: Tue Dec 11, 2007 4:24 pm
Re: The differences of the bayesian classifier and bayesian networks
Bayesian classifier and Bayesian network are two related concepts but they mean different things. Bayesian classifier is a model based on Bayesian methods aiming at classification. Bayesian networks are great classifiers. You have described a naive Bayes (class is the only parent of every feature node), a TAN model, and a general unrestricted Bayesian network. They are all Bayesian networks and they can be all used as classifiers. Bayesian networks can be used for tasks other than classification, for example diagnosis or prognosis. For that purpose one could in theory apply each of the structures that you mentioned (naive, TAN or general). So, the two concepts are related but describing different dimensions of the problem. Does this help?
Marek
Marek
Re: The differences of the bayesian classifier and bayesian networks
Dear Marek
Your reply is a great help to me, Thank you very much!
Your reply is a great help to me, Thank you very much!