1. Dynamic Bayesian Networks
Representation
Probabilistic
Graphical
Models
Template Models
Dynamic Bayesian Networks

2. Template Transition Model
Weather
Weather’
Velocity
Velocity’
Location
Location’
Failure
Failure’
Obs’
Time slice t
Time slice t+1

3. Initial State Distribution
Weather0
Velocity0
Location0
Failure0
Obs0
Time slice 0

4. Ground Bayesian Network
Weather0
Weather1
Weather2
Velocity0
Velocity1
Velocity2
Location0
Location1
Location2
Failure0
Failure1
Failure2
Obs0
Obs1
Obs2
Time slice 0
Time slice 1
Time slice 2

5. Tim Huang, Dieter Koller, Jitendra Malik, Gary Ogasawara, Bobby Rao, Stuart Russell, J. Weber

6. Dynamic Bayesian Network
A transition model over X1,…,Xn is specified via
A dynamic Bayesian network is specified via

7. Ground Network

8. Hidden Markov Models s1 s2 s3 s4 S S’ S1 O1 S0 S2 O2 S3 O3 O’ 0.5 0.7
0.3
0.4
0.6
0.1
0.9

9. Hidden Markov Models s1 s2 s3 s4 S S’ S1 O1 S0 S2 O2 S3 O3 O’ 0.5 0.7
0.3
0.4
0.6
0.1
0.9

10. Consider a smoke detection tracking application, where we have 3 rooms connected in a row. Each room has a true smoke level (X) and a smoke level (Y) measured by a smoke detector situated in the middle of the room. Which of the following is the best DBN structure for this problem?
X’1
Y’1 X1
X’2
Y’2 X2
X’3
Y’3 X3
X’1
Y’1 X1
X’2
Y’2 X2
X’3
Y’3 X3
X’1
Y’1 X1
X’2
Y’2 X2
X’3
Y’3 X3
X’1
Y’1 X1
X’2
Y’2 X2
X’3
Y’3 X3

11. Consider an application, where we have 3 sources, each making sound (X) simultaneously (e.g., a TV, a blender, and a ringing cellphone). We want to separate the observed aggregate signal (Y) into its unobserved constituent signals. Which of the following is the best DBN structure for this problem?
X’1 X1
X’2 X2
X’3 Y X3 X1
X’1 X2
X’2 X3
X’3 Y
X’1
Y’1 X1
X’2
Y’2 X2
X’3
Y’3 X3
X’1
Y’1 X1
X’2
Y’2 X2
X’3
Y’3 X3

12. Consider a situation where we have two people in a conversation, each wearing a sensitive lapel microphone. We want to separate each person’s speech (X) using the signal (Y) obtained from their microphone. Which of the following is the best DBN structure for this problem? X1
X’1 X1
X’1
Y’1
Y’1 X2
X’2 X2
X’2
Y’2
Y’2 X1
X’1 X1
X’1
Y’1 X2
X’2
Y’1 X2
X’2
Y’2
Y’2

13. Summary
DBNS are a compact representation for encoding structured distributions over arbitrarily long temporal trajectories
They make assumptions that may require appropriate model (re)design:
Markov assumption
Time invariance