Consider a distribution defined over binary variables: p(a,b,c)=p(a|b)p(b|c)p(c)with

?(? = ?? | ? = ??) = 0.3 , ?(? = ?? | ? = ??) = 0.2 , ?(? = ?? | ? = ??) = 0.75

?(? = ?? | ? = ??) = 0.1 ,

?(? = ??) = 0.4,

What is the most likely joint configuration? That is

argmax

!,#,$

?(?,

?, ?)

?

Hint: It is not acceptable to just naively work out the 8 possible states to solve the

problem. Nave approach is only feasible for this example but not for a general problem

with many variables. Instead, you must use the max-product algorithm to solve this

problem.