Dynamic Bayesian Networks

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Daphne Koller Template Models Dynamic Bayesian Networks Probabilistic Graphical Models Representation

description

Representation. Probabilistic Graphical Models. Template Models. Dynamic Bayesian Networks. Template Transition Model. Weather. Weather’. Velocity. Velocity’. Location. Location’. Failure. Failure’. Obs’. Time slice t. Time slice t+1. Initial State Distribution. Weather 0. - PowerPoint PPT Presentation

Transcript of Dynamic Bayesian Networks

Page 1: Dynamic Bayesian Networks

Daphne Koller

Template Models

DynamicBayesianNetworks

ProbabilisticGraphicalModels

Representation

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Daphne Koller

Template Transition Model

Location’

Failure’

Obs’

Location

Failure

Time slice t Time slice t+1

Velocity Velocity’

Weather Weather’

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Daphne Koller

Location0

Failure0

Time slice 0

Velocity0

Weather0

Obs0

Initial State Distribution

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Daphne Koller

Location1

Failure1

Obs1

Location0

Failure0

Time slice 0 Time slice 1

Velocity0 Velocity1

Weather0 Weather1

Location2

Failure2

Obs2

Velocity2

Weather2

Time slice 2

Obs0

Ground Bayesian Network

Page 5: Dynamic Bayesian Networks

Daphne KollerTim Huang, Dieter Koller, Jitendra Malik, Gary Ogasawara, Bobby Rao, Stuart Russell, J. Weber

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Daphne Koller

Dynamic Bayesian Network• A transition model over X1,…,Xn is specified

via

• A dynamic Bayesian network is specified via

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Daphne Koller

Ground Network

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Daphne Koller

S’

O’

S

Hidden Markov Models

S1

O1

S0 S2

O2

S3

O3

s1 s2 s3 s4

0.5

0.50.7

0.3

0.4

0.6

0.1

0.9

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Daphne Koller

S’

O’

S

Hidden Markov Models

S1

O1

S0 S2

O2

S3

O3

s1 s2 s3 s4

0.5

0.50.7

0.3

0.4

0.6

0.1

0.9

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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

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Daphne Koller

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