The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
CSIT 5220
Page 1
Recap of L04: Model Building
Catching the structure
CSIT 5220
Tradeoff between faithfulness and model complexity
CSIT 5220
Causal Markov Assumption Not Always True
CSIT 5220
Use of mediating variables to ease probability assessment
P(OH0)
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
CSIT 5220: Reasoning and Decision under Uncertainty
Lecture 5: Inference in Bayesian Networks: The VE Algorithm
Nevin L. Zhang
lzhang@cse.ust.hk
Department of Computer Science and Engineering
The Hong Kong University of Science and Technology
Nevin L. Zha
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
CSIT 5220
Page 1
Lecture 04: Building Models
Objective
Reading
Discuss practical considerations in model building
Jensen and Nielsen, Chapter 3
Outline
Catching the structure
Determining probabilities
Reducing the number of parameters
Other Issues
CSIT 52
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
CSIT 5220: Reasoning and Decision under Uncertainty
Lecture 2: Bayesian Networks
Nevin L. Zhang
lzhang@cse.ust.hk
Department of Computer Science and Engineering
The Hong Kong University of Science and Technology
Nevin L. Zhang (HKUST)
Bayesian Networks
1
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
CSIT 5220: Reasoning and Decision under Uncertainty
Lecture 3: DSeparation
Nevin L. Zhang
lzhang@cse.ust.hk
Department of Computer Science and Engineering
The Hong Kong University of Science and Technology
Nevin L. Zhang (HKUST)
Bayesian Networks
1 / 23
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
CSIT 5220
Page 1
Recap of Lecture 2
From Joint Distributions to Bayesian networks
CSIT 5220
Chain Rule
http:/en.wikipedia.org/wiki/Chain_rule_(probability)
Chain rule permits the calculation of the joint distribution of a set of
random variables using con
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
CSIT 5220: Reasoning and Decision under Uncertainty
Lecuture 1: Basics of Multivariate Probability
Nevin L. Zhang
lzhang@cse.ust.hk
Department of Computer Science and Engineering
The Hong Kong University of Science and Technology
Nevin L. Zhang (HKUST)
Ba
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
Solutions for Bayesian networks and decision graphs
(second edition)
Finn V. Jensen and Thomas D. Nielsen
May 19, 2008
Solution for exercise 4.1
P (A = yD = y) = 0.197; P (C = yD = y) = 0.531.
Solution for exercise 4.2
Solution for exercise 4.3
(i) P (A
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
CSIT 5220
Page 1
Recap of Lecture 1
Basics of Multivariate Probability
Mathematical definitions
Interpretation of probability
Multivariate probability
CSIT 5220
Page 2
Probability w.r.t Process with Uncertain Outcome
CSIT 5220
Page 3
Example
CSIT 5220
Pag
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
Solutions for Bayesian networks and decision graphs
(second edition)
Finn V. Jensen and Thomas D. Nielsen
August 23, 2007
Solution for exercise 3.1
There are two information variables, English Grade and Math Grade and three
hypothesis variables, Prob. Gra
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
Solutions for Bayesian networks and decision graphs
(second edition)
Finn V. Jensen and Thomas D. Nielsen
September 6, 2007
Solution for exercise 1.1
Define B 0 = B \ (A B). We immediately have
A B0 = ,
(1)
A B0 = A B ,
(2)
(A B) B 0 = B .
(3)
(A B) B 0 =
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
Solutions for Bayesian networks and decision graphs
(second edition)
Finn V. Jensen and Thomas D. Nielsen
February 18, 2009
Solution for exercise 2.1
(i)
2 1 1
3, 3, 2.
(ii) Close to zero. Notice that the certainty resulting from the combined
action is mu
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
Solutions for Bayesian networks and decision graphs
(second edition)
Finn V. Jensen and Thomas D. Nielsen
October 14, 2008
Solution for exercise 6.1
Setting the derivative equal to zero we get the equation
80 79 (1 )20 80 20(1 )19 = 0.
This holds if = 0,
The Hong Kong University of Science and Technology
Resoning and Decision
SCIENCE 5220

Summer 2015
Solutions for Bayesian networks and decision graphs
(second edition)
Finn V. Jensen and Thomas D. Nielsen
August 16, 2007
Solution for exercise 5.1
Solution for exercise 5.2
Solution for exercise 5.3
Solution for exercise 5.4
Solution for exercise 5.5
Sol