Page 1
Part II − Application to Markov
Structures
Page 2
A Motivating Example
✕ ✕✕ ✕✕ ✕✕ ✕
Page 3
Conditional Mutual Independence
Page 7
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Page 8
Full Conditional Mutual Independence
(FCMI)
Page 18
Illustration of Im(K)
Page 19
Illustration of Im(K)
Page 29
The Implication Problem
Page 30
The Implication Problem
Page 31
The Implication Problem
Page 32
The Implication Problem
Page 33
The Implication Problem
Page 41
Markov Random Field
Page 42
Graph Theory Terminologies
Page 43
Graph Theory Terminologies
Page 44
Graph Theory Terminologies
Page 45
Graph Theory Terminologies
Page 46
Global Markov Property
Page 47
Global Markov Property
Page 48
Global Markov Property
Page 49
Global Markov Property
Page 50
FCMIs Specified by a MRF
Page 51
FCMIs Specified by a MRF
Page 52
FCMIs Specified by a MRF
Page 53
FCMIs Specified by a MRF
Page 54
FCMIs Specified by a MRF
Page 55
Type I and Type II Atoms
Page 56
Type I and Type II Atoms
Page 57
Type I and Type II Atoms
Page 58
Type I and Type II Atoms
Page 60
A Graph-Theoretic Analog
Page 64
Special Properties of a Markov Chain
Page 65
Special Properties of a Markov Chain
Page 66
Special Properties of a Markov Chain
Page 68
Construction of Information Diagram
Page 69
Construction of Information Diagram
Page 70
Construction of Information Diagram
Page 71
Construction of Information Diagram
Page 72
Construction of Information Diagram
Page 73
Nonnegativity of µ*
Page 74
Nonnegativity of µ*
Page 75
Nonnegativity of µ*
Page 76
A Formal Justification