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CS181 Lecture 14: Bayesian

Networks: Applications and

Inference

David C. Parkes

Applications

• Liver diagnosis
  • reformulate; Noisy-OR
• TrueSkill (Xbox 360)
  • continuous RVs; approximate inference
• Coordinate and Notify
  • information over-load tools
• Transportation modes
  • learn routine, assist cogn. impaired people
• Early swine Flu detection

• Hepar II
• Used for diagnosis of liver disorders
• Only 505 records. 60-70 nodes

First Idea: Reformulate

Onisko et al.

(HEPAR II)

single diagnosis

multiple

diagnosis

(less parameters,

since fewer parents)

Second Idea: Efficient CPTs

3 parameters

NOISY-OR

qC = P(:F | C, :Fl, :M)=0.

qFl = P(:F | Fl, :C, :M)=0.

qM = P(:F | M, :Fl, :C)=0.

But, kind of like an “OR”?

P(:F | C, M,:Fl) = qC£qM = 0.

P(:F | C, Fl,:M) = qC£qFl = 0.

P(:F | :C,:Fl,:M) = 1 …

Cold Flu Malaria

Fever

23 parameters

NOISY-OR

• HEPAR II
• 27 of the 62 nodes identified as Noisy-OR

by experts

• Further reduced number of parameters

from 3714 to 1488

• Achieved 5% reduction in error rate

• TrueSkill vs ELO method

ELO:

pi » N(P | ¹i, ¾i^2 )

¹i is skill

update using maximum

likelihood based on

estimated skill of

opponent

Weakness:

doesn’t account for

confidence in skill of

opponent

Continuous RVs in a Graphical Model

subsidy harvest

cost

buy

P(S=1)

Boolean 1 param

Gaussian model N (H | ¹h, ¾^2 h) continuous 2 params

Probit model

P(B | C) = ©((¹b – C) / ¾b )

Boolean (but w/ continuous parent) 2 parameters

Linear-Gaussian model S=1: N (C | at H + bt, ¾^2 t) S=0: N (C | af H + bf, ¾^2 f) continuous 6 parameters

cost

prob buy

¹b

Comment: Full Bayes

Y

X 1 X 2

μT 2

μF 2

μT 1

μF 1

μY

5 parameters

X 1

Comment: Full Bayes

Y

X 1 X 2

μT 2

μF 2

Beta(μT 2 | ®T 2 , ¯T 2 )

Beta(μF 2 | ®F 2 , ¯F 2 )

μT 1

μF 1

μY

7 parameters

Notify Horvitz et al.

Temporal attention model providing probability distribution over

user’s workload and task for selective filtering of messages

Transportation routines

Fox et al.

estimates user’s goal (e.g., workplace, home, friend) and trip segments taking

novelty detection (disables middle layer)

transportation mode speed location

observations: GPS

used to help

cognitively-

impaired people

Swine Flu Detection

(Central Institute for Animal Disease Control, The Netherlands)

van der Gaag et al.