Introduction to Probabilistic Graphical Models Problem Set #3
1
Probabilistic Graphical Models, Spring 2009
Problem Set #3
1. (a) Prove the following theorem: Let G1 and G2 be two graphs over X . If they have the
same skeleton and the same set of v-struct
Introduction to Probabilistic Graphical Models Problem Set #1 Solutions
1
Probabilistic Graphical Models, Spring 2009
Problem Set #1 Solution : Probability Review
1. After your yearly checkup, the doctor has bad news and good news. The bad news is
that yo
Introduction to Probabilistic Graphical Models Problem Set #1
1
Probabilistic Graphical Models, Spring 2009
Problem Set #1: Probability Review
Note: In the questions below, P is a joint probability distribution over the speciﬁed variables.
For example, P
1
Introduction to Probabilistic Graphical Models
Lecturer: Eran Segal
Problem set 2 - Solutions
1. General notes:
• Please note that y P (X|Y = y) = P (X). Moreover, it can be easily veriﬁed that
y P (X|Y = y) might not even represent a valid distribution
Introduction to Probabilistic Graphical Models Problem Set #2
1
Probabilistic Graphical Models, Spring 2009
Problem Set #2
1. (a) Prove that the Weak Union property holds for all distributions P :
(X ⊥ Y, W | Z) =⇒ (X ⊥ Y | Z, W )
(b) Prove the Contractio
1
Introduction to Probabilistic Graphical Models
December 13, 2007
Problem set 3 - Solutions
Lecturer: Eran Segal
1. (a) Prove the following theorem: Let G1 and G2 be two graphs over X . If they have the
same skeleton and the same set of v-structures then
1
December 26, 2006
Introduction to Probabilistic Graphical Models
Problem set 4 - Solutions
Lecturer: Eran Segal
1. (a) This can be done by summing out the variables that we wish to remove and incorporating their eﬀects into the leak noise parameter. The
Introduction to Probabilistic Graphical Models Problem Set #4
1
Probabilistic Graphical Models, Spring 2009
Problem Set #4
1. Consider the network shown in the ﬁgure, where we assume that all variables are binary,
and that the Fi variables in the second l
Stacks
CS 308 Data Structures
What is a stack?
It is an ordered group of homogeneous items of elements. Elements are added to and removed from the top of the stack (the most recently added items are at the top of the stack). The last element to be added