1. Preliminaries: Distributions
Probabilistic
Graphical
Models
Introduction
Preliminaries: Distributions

2. Joint Distribution Intelligence (I) Difficulty (D) Grade (G) I D G
Prob. i0 d0 g1
0.126 g2
0.168 g3 d1
0.009
0.045 i1
0.252
0.0224
0.0056
0.06
0.036
0.024
Intelligence (I)
i0 (low), i1 (high),
Difficulty (D)
d0 (easy), d1 (hard)
Grade (G)
g1 (A), g2 (B), g3 (C)
Probability space
Parameters and independent parameters

3. Conditioning condition on g1 I D G Prob. i0 d0 g1 0.126 g2 0.168 g3 d1
0.009
0.045 i1
0.252
0.0224
0.0056
0.06
0.036
0.024
condition on g1

4. Conditioning: Reduction
Prob. i0 d0 g1
0.126 d1
0.009 i1
0.252
0.06

5. Conditioning: Renormalization
Prob. i0 d0 g1
0.126 d1
0.009 i1
0.252
0.06 I D
Prob. i0 d0
0.282 d1
0.02 i1
0.564
0.134
P(I, D, g1)
P(I, D | g1)
0.447
0.447

6. Marginalization Marginalize I I D Prob. i0 d0 0.282 d1 0.02 i1 0.564
0.134 D
Prob. d0
0.846 d1
0.154