Chapter 2 Bayesian Networks:
Representation
2016 Fall
Jin Gu, Michael Zhang
Outlines
Conditional independence
Conditional parameterization
Nave Bayes model
Bayesian networks
BNs and local independences
I-map and factorization
d-separation
From distrib

Assignment #1
[Seven problem sets in this assignment]
1. Prove the following properties of Conditional Independence:
1) Decomposition:
X Y ,W | Z X Y | Z
2) Weak union:
X Y ,W | Z X Y | Z ,W
3) Contraction:
X W | Z , Y & X Y | Z X Y ,W | Z
2. In an

Chapter 1 Introduction to
Probabilistic Graphical Models
2016 Fall
Jin Gu, Michael Zhang
Outlines
Model the world with probability
Model the world with graph
Probabilistic graphical models (PGMs)
Some applications of different PGMs
Course schedule (homew

PGM-Assignment #2
1. Consider the following Bayesian Network.
Figure 1: A Bayesian network witn qualitative influences
Assume that all variables are binary-valued. We do not know the CPDs, but do know how each random variable
qualitatively affects its chi