1. Learning
Probabilistic
Graphical
Models
Overview
Learning Problems

2. Learning Data Network dataset of instances D={d[1],...d[m]}
domain expert
Declarative representation
Network
Learning
elicitation

3. Learning Tasks Known structure Unknown structure Latent variables
Fully observable data
Partly observable data

4. Known Structure, Complete DataX1 X2 X1 X2
Inducer
Initial network Y Y X1 X2 Y
x10
x21 y0
x11
x20 y1
P(Y|X1,X2) X1 X2 y0 y1
x10
x20 1
x21
0.2
0.8
x11
0.1
0.9
0.02
0.98
Input Data

5. Unknown Structure, Complete DataX1 X2 X1 X2
Inducer
Initial network Y Y X1 X2 Y
x10
x21 y0
x11
x20 y1
P(Y|X1,X2) X1 X2 y0 y1
x10
x20 1
x21
0.2
0.8
x11
0.1
0.9
0.02
0.98
Input Data

6. Known Structure, Incomplete DataX1 X2 X1 X2
Inducer
Initial network Y Y X1 X2 Y ?
x21 y0
x11
x10
x20 y1
P(Y|X1,X2) X1 X2 y0 y1
x10
x20 1
x21
0.2
0.8
x11
0.1
0.9
0.02
0.98
Input Data

7. Unknown Structure, Incomplete DataX1 X2 X1 X2
Inducer
Initial network Y Y X1 X2 Y ?
x21 y0
x11
x10
x20 y1
P(Y|X1,X2) X1 X2 y0 y1
x10
x20 1
x21
0.2
0.8
x11
0.1
0.9
0.02
0.98
Input Data

8. Latent Variables, Incomplete DataH X1 X2 X1 X2
Inducer
Initial network Y Y X1 X2 Y ?
x21 y0
x11
x10
x20 y1
P(Y|X1,X2) X1 X2 y0 y1
x10
x20 1
x21
0.2
0.8
x11
0.1
0.9
0.02
0.98
Input Data

9. Learning Tasks: BNs Known structure Unknown structure Latent variables
Fully observable data
Partly observable data

10. Learning Tasks: MNs Known structure Unknown structure Latent variables
Fully observable data
Partly observable data

11. Target Tasks Probabilistic queries about new instances
Specific tasks (e.g., classification)
Knowledge discovery
Direct vs indirect dependencies
Possibly directionality of edges
Directionality of influence
Hidden variables

12. Performance Metrics Distance of learned model to true distribution
Evaluate performance by how well the network estimates probability of new examples (“test data”)
Task-specific accuracy on test set
Distance of learned structure or parameters to true a ground truth model
Often compare to (limited) prior knowledge

13. END END END