by qxin001 » Fri May 26, 2017 11:50 am
Concept learning for Bayesian Network:
1.Bayes Rule P(A|B)=P(B|A)P(A)/P(B)
2.Likelihood-How probable is the evidence given that our hypothesis is true?
Prior-How probable was our hypothesis before observing the evidence?
Posterior-How probable is our hypothesis given the oberserved evidence?
Marginal-How probable is the new evidence under all possible hypotheses?
P(H|e)=P(e|H)P(H)/P(e)
what we want to know : p(s|x) posterior
what we should know: p(s|x)=p(x|s)p(s) likelihood *prior
background knowledge: p(s|x)=p(x|s)p(s) p(x|s) is maximum likelihood. p(s) is assumption.
3.A Bayesian Network consists below:
A set of variables and a set of direct edges between variables
Each variables has a finite set of mutually exclusive states
The variable and direct edge form a DAG (directed acyclic graph)
To each variable A with parents B1, B2 ..Bn there is attached a conditional probability table P(A| B1, B2 .. Bn) ------------reference from [Jensen, 1996]
Jessen F., An Introduction of Bayesian Network, Springer-Verlag,1996
4.Three Bauesian Network Structure connection
diverging connection P(A,B,C)=P(B|C)P(A|C)P(C)
serial connection P(A,B,C)=P(B|C)P(C|A)P(A)
converging connection P(A,B,C)=P(C|A,B)P(B)P(A)
5.Bayesian belief network For instance, if we already know a CPT of LungCancer, we could calculate the probability -P("Smoker")*P("FamilyHistory")*P("Lungcancer"|("FamilyHistory,Smoker")). We will get more accurate result.If each conditional probability is unknown, we should use EM algorithm or others. If the data structure is unknown, then we should use K2 algorithm(greedy search) to solve this problem based on the data we already know.