1. Flow of Probabilistic Influence
Representation
Probabilistic
Graphical
Models
Bayesian Networks
Flow of Probabilistic Influence

2. When can X influence Y? X → Y X ← Y X → W → Y X ← W ← Y X ← W → Y
Intelligence
Difficulty
Grade
Letter
SAT
pairs

3. Active Trails A trail X1 ─ … ─ Xn is active if:
it has no v-structures Xi-1 → Xi ← Xi+1

4. When can X influence Y Given evidence about Z
X → Y
X ← Y
X → W → Y
X ← W ← Y
X ← W → Y
X → W ← Y
W  Z
W  Z
Intelligence
Difficulty
Grade
Letter
SAT
pairs

5. When can X influence Y given evidence about Z
S ― I ― G ― D allows influence to flow when:
Intelligence
Difficulty
Grade
Letter
SAT
longer trails

6. Active Trails A trail X1 ─ … ─ Xn is active given Z if:
for any v-structure Xi-1 → Xi ← Xi+1 we have that Xi or one of its descendants Z
no other Xi is in Z