9 - Bayesian Networks

Question 1

Boolean Random Variables

Answer 1

take the values true or false- think of the event as occurring or not occurring

Question 2

What are Bayesian Networks?

Answer 2

A Bayesian network (BN) is a probabilistic graphical model for representing knowledge about an uncertain domain where each node corresponds to a random variable and each edge represents the conditional probability for the corresponding random variables

Question 3

What is Conditional Independence?

Answer 3

situations where an observation is irrelevant or redundant when evaluating the certainty of a hypothesis

Question 4

What is Joint Probability Distribution?

Answer 4

Joint probability is a statistical measure that calculates the likelihood of two events occurring together and at the same point in time.

Question 5

Explain Bayes Nets Formalized

Answer 5

is an augmented directed acyclic graph, represented by the pair V, E where:
*V is a set of vertices. *E is a set of directed edges joining vertices. No loops of any length are allowed

Question 6

How would you build a bayers net?

Answer 6

1.Choose a set of relevant variables and an ordering for them.
2.Assume they’re called X1, …,Xm(where X1 is the first in the ordering, X2 is the second, etc.)
3.For i= 1 to m:
i.Add the Xi node to the network
ii.Set Parents(Xi)to be a minimal subset of {X1…Xi-1} such that we have conditional independence of Xiand all other members of {X1…Xi-1} given Parents(Xi)
iii.Define the probability table of P(Xi=kAssignments of Parents(Xi))