Classifying new instance with bayesian net

1
votes

Say I have the following bayesian network:

enter image description here

And I want to classify a new instance on wether H=true or H=false, the new instance looks e.g. like this: Fl=true, A=false, S=true, and Ti=false.

How can I classify the instance with respect to H?

I can compute the probability by multiplying the probabilities from the tables:

0.4 * 0.7 * 0.5 * 0.2 = 0.028

What does this say about whether the new instance is a positive instance H or not?

EDIT I will try the compute the probability according to Bernhard Kausler's suggestion:

So this is Bayes' rule: P(H|S,Ti,Fi,A) = P(H,S,Ti,Fi,A) / P(S,Ti,Fi,A)

to compute de denominator: P(S,Ti,Fi,A) = P(H=T,S,Ti,Fi,A)+P(H=F,S,Ti,Fi,A) = (0.7 * 0.5 * 0.8 * 0.4 * 0.3) + (0.3 * 0.5 * 0.8 * 0.4 * 0.3) =0.048

P(H,S,Ti,Fi,A) = 0.336

so P(H|S,Ti,Fi,A) = 0.0336 / 0.048 = 0.7

now i compute P(H=false|S,Ti,Fi,A) = P(H=false,S,Ti,Fi,A) / P(S,Ti,Fi,A) we already have the value for P(S,Ti,Fi,A´. I's ´0.048.

P(H=false,S,Ti,Fi,A) =0.0144

so P(H=false|S,Ti,Fi,A) = 0.0144 / 0.048 = 0.3

the Probability for P(H=true,S,Ti,Fi,A) is the highest. so the new instance will be classified as H=True

Is this correct?

Addition: We do not need to calculate P(H=false|S,Ti,Fi,A) because it is 1 - P(H=true|S,Ti,Fi,A).

1
machine-learningclassificationbayesian-networks

1 Answers

1
votes

So, you want to compute the conditional probability P(H|S,Ti,Fi,A). To do that, you have to use Bayes' rule:

P(H|S,Ti,Fi,A) = P(H,S,Ti,Fi,A) / P(S,Ti,Fi,A)

where

P(S,Ti,Fi,A) = P(H=T,S,Ti,Fi,A)+P(H=F,S,Ti,Fi,A)

You then calculate both conditional probabilities P(H=T|S,Ti,Fi,A) and P(H=F|S,Ti,Fi,A) and make a prediction according to which probability is higher.

Just multiplying up the numbers like you did won't help and doesn't even give you a proper probability since the product is not normalized.