Question

Suppose that we have the data below, where Stolen is the target attribute that consists of binary values (yes or no). Color Type Origin Stolen red sports domestic yes red sports domesticno red sports domestic yes yellow sports domestic no yellow sports imported yes yellow Suy imported no yellow suy imported yes yellow suv domesticno red Suy imported no red sports imported yes You have a naive bayes model and a new test instance with attributes color=red, type=suv and origin=imported. What would be the predicted label by the naive bayes model for the given test instance? Write down your calculations step by step. There is no need to use latex in this question. You may show your calculations as P(stolen=yes|color=red...) = (...)/(...) etc.

Answer 1

-->

Probability of Stolen = yes is given by :

P(Stolen=yes/color= red, type=suv, origin=imported)

= P(color= red/Stolen=yes) * P(type= suv/Stolen=yes)

    * P(origin=imported/Stolen=yes) * P(Stolen=yes)

= 3/5 * 1/5 * 3/5 * 1/2

= 0.036

-->

Similarly Probability of Stolen = no is given by :

P(Stolen=no/color= red, type=suv, origin=imported)

= P(color= red/Stolen=no) * P(type= suv/Stolen=no)

    * P(origin=imported/Stolen=no) * P(Stolen=no)

= 2/5 * 3/5 * 2/5 * 1/2

= 0.048

--> The Stolen = no has higher probability. So, Answer is "no"