PGM, Fall 2006
1
Problem Set #6
Due on Wednesday, December 27
1. A polytree is a singly-connected, directed graph (singly-connected graph is a graph that
does not contain any undirected cycles).
(a) Show that variable elimination on polytrees can be perfo
Introduction to Probabilistic Graphical Models Problem Set #7
1
Probabilistic Graphical Models, Fall 2006
Problem Set #7
1. In this problem you will show that the family of mixture of Dirichlet priors is conjugate to
the multinomial distribution.
(a) Cons
Introduction to Probabilistic Graphical Models Problem Set #8
1
Probabilistic Graphical Models, Fall 2006
Problem Set #8
1. Consider a graph G which is I-equivalent to G , and assume we use table CPDs.
(a) Show that for any choice of data set D, we have t
Introduction to Probabilistic Graphical Models Problem Set #8
1
Probabilistic Graphical Models, Fall 2006
Problem Set #8 - Solution
1. Consider a graph G which is I-equivalent to G , and assume we use table CPDs.
(a) Show that for any choice of data set D
1
Introduction to Probabilistic Graphical Models
Lecturer: Eran Segal
Problem set 7 - Solutions
1. In this problem you will show that the family of mixture of Dirichlet priors is conjugate to
the multinomial distribution.
(a) Consider the simple possibly-
Introduction to Probabilistic Graphical Models Final Exam, March 2007
1
Probabilistic Graphical Models Final Exam
Please ll your name and I.D.:
Name: .
I.D.: .
Duration: 3 hours.
Guidelines:
1. The test is composed of ve questions. The credit for each que
Introduction to Probabilistic Graphical Models Problem Set #8
1
Probabilistic Graphical Models, Spring 2009
Problem Set #8
1. Consider a graph G which is I-equivalent to G , and assume we use table CPDs.
(a) Show that for any choice of data set D, we have
1
Introduction to Probabilistic Graphical Models Problem Set #8
Probabilistic Graphical Models, Spring 2009
Problem Set #8 - Solution
1. Consider a graph G which is I-equivalent to G , and assume we use table CPDs.
(a) Show that for any choice of data set
1
Introduction to Probabilistic Graphical Models
Spring 2009
Problem set 5 - Solutions
Lecturer: Eran Segal
1. (a) Answer:
Suppose for a contradiction that we have sepH (X, Y | Z), but not d-sepG (X, Y | Z).
This means that in G with Z observed, there exi
PGM, Spring 2009
1
Problem Set #6
1. A polytree is a singly-connected, directed graph (singly-connected graph is a graph that
does not contain any undirected cycles).
(a) Show that variable elimination on polytrees can be performed in linear time, assumin
PGM, Fall 2006
1
Problem Set #6 - Solution
1. A polytree is a singly-connected, directed graph (singly-connected graph is a graph that
does not contain any undirected cycles).
(a) Show that variable elimination on polytrees can be performed in linear time
Introduction to Probabilistic Graphical Models Problem Set #9
1
Probabilistic Graphical Models, Spring 2009
Problem Set #9
1. Recall that structural EM (SEM) uses the existing candidate Bayesian network to complete
the data, and then uses the completed da
1
Introduction to Probabilistic Graphical Models
December 13, 2006
Problem set 9 - Solutions
Lecturer: Eran Segal
1. Answer:
Recall that structural EM (SEM) uses the existing candidate Bayesian network to complete
the data, and then uses the completed dat
Introduction to Probabilistic Graphical Models Problem Set #10
1
Probabilistic Graphical Models, Fall 2006
Problem Set #10
1
Importance Sampling
Let G be a network (either Bayesian or Markov)
Let X1 , X2 , .Xn be some ordering (not necessary topological)
Introduction to Probabilistic Graphical Models Problem Set #7
1
Probabilistic Graphical Models, Spring 2009
Problem Set #7
1. In this problem you will show that the family of mixture of Dirichlet priors is conjugate to
the multinomial distribution.
(a) Co
Introduction to Probabilistic Graphical Models Problem Set #5
1
Probabilistic Graphical Models, Spring 2009
Problem Set #5
1. In class we noted that a clique separator (sepset, see page 228) d-separates the BN graph
into two conditionally independent piec
1
Introduction to Probabilistic Graphical Models
Problem set 10 - Solutions
Lecturer: Eran Segal
1
Importance Sampling
Let G be a Bayesian network, E = e an observation, and X1 , . . . , Xk be some ordering (not
necessarily topological) of the unobserved