[Thrun] So we’re now ready to define Bayes networks in a more general way. Bayes networks define probability distributions over graphs or random variables. Here is an example graph of 5 variables, and this Bayes network defines the distribution over those 5 random variables. Instead of enumerating all possibilities of combinations of these 5 random variables, the Bayes network is defined by probability distributions that are inherent to each individual node. For node A and B, we just have a distribution P of A and P of B because A and B have no incoming arcs. C is a conditional distribution conditioned on A and B. D and E are conditioned on C. The joint probability represented by a Bayes network is the product of various Bayes network probabilities that are defined over individual nodes where each node’s probability is only conditioned on the incoming arcs. So A has no incoming arc; therefore, we just want it P of A. C has 2 incoming arcs, so we define the probability of C conditioned on A and B. And D and E have 1 incoming arc that’s shown over here. The definition of this joint distribution by using the following factors has one really big advantage. Whereas the joint distribution over any 5 variables requires 2 to the 5 minus 1, which is 31 probability values, the Bayes network over here only requires 10 such values. P of A is one value, for which we can derive P of not A. Same for P of B. P of C given A B is derived by a distribution over C conditioned on any combination of A and B, of which there are 4 of A and B as binary. P of D given C is 2 parameters for P of D given C and P of D given not C. And the same is true for P of E given C. So if you add those up, you get 10 parameters in total. So the compactness of the Bayes network leads to a representation that scales significantly better to large networks than the common natorial approach which goes through all combinations of variable values. That is a key advantage of Bayes networks, and that is the reason why Bayes networks are being used so extensively for all kinds of problems. So here is a quiz. How many probability values are required to specify this Bayes network? Please put your answer in the following box.

This video should be at the begining of the introduction to Bayes Networks, not at the end!

thanks

you see how it is (2^5) -1 yeah? how come there is a -1 and its not just 2^5. don't really understand…

Is this part of a course? Where is the course overview?

Yes, there are hundreds of parts of this course, but the channel didn't organize trhought a playlist. There are user playlist. Type "Unit 0w". Warning, is really very hard, much much math.

I think he counting from 0..

so he subract 1 from total

I think he is wrong,,

for n nodes, you will have 2^n combinations…

Check Wiki example here..

http://en.wikipedia.org/wiki/Joint_probability_distribution#Example

Correct me if I am wrong…

Probabity Values: 2^6-1=63

Joint Probability: 13

what is the correct ans ?? please??

do we include parameter into the equation?

I think it is 11. But Ms. D thinks it is 13. We both are stupid, btw

Total probability values = 63

Using Joint Probability Distribution: 13 values

what would be the probability of B/C for example?

what about B/E ?