next up previous
Next: d-separation I [2 P] Up: MLA_Exercises_2009 Previous: Exercises

Conditional Independence [2 P]

a)
[1 P] Construct a probability distribution $ P(A,B,C)$ that disproves

$\displaystyle P(A,B) = P(A) P(B) \rightarrow P(A,B\vert C) = P(A\vert C) P(B\vert C) .$

Illustrate the phenomenon of 'explaining away'.

b)
[1 P] Construct two different probability distributions $ P(A,B,C)$ (that correspond to two different Bayesian Networks) that disprove

$\displaystyle P(A,B\vert C) = P(A\vert C) P(B\vert C) \rightarrow P(A,B) = P(A) P(B).$



Haeusler Stefan 2010-01-26