a. darwiche bayesian networks. a. darwiche bayesian network battery age alternator fan belt battery...

A. Darwiche

Bayesian NetworksBayesian Networks

A. Darwiche

Bayesian NetworkBayesian NetworkBattery Age Alternator Fan Belt

BatteryCharge Delivered

Battery Power

Starter

Radio Lights Engine Turn Over

Gas Gauge

Gas

Fuel Pump Fuel Line

Distributor

Spark Plugs

Engine Start

A. Darwiche

Bayesian NetworkBayesian NetworkBattery Age Alternator Fan Belt

BatteryCharge Delivered

Battery Power

Starter

Radio Lights Engine Turn Over

Gas Gauge

Gas

Fuel Pump Fuel Line

Distributor

Spark Plugs

Engine Start

Pr(Lights=ON | Battery-Power=OK) = .99

ON OFF

OK

WEAK

DEAD

Lights

Bat

tery

Pow

er

.99 .01

.20 .800 1

.99

θ1 + θ2 = 1

A. Darwiche

A. Darwiche

No children

01

62.937.1

0.37 ± 0.48

Children ages 12-17

01

82.317.7

0.18 ± 0.38

Children ages 6-11

01

80.619.4

0.19 ± 0.4

Education

Under K12K12Some collegeBachelor degreeMaster or PhD

1.3410.935.133.019.6

3.59 ± 0.97

Marital Status

Single never marriedMarriedDivorced or separatedWidowedDomestic partnership

24.460.210.21.403.79

2 ± 0.86

Income

0 to 2000020000 to 3000030000 to 4000040000 to 5000050000 to 6000060000 to 7500075000 to 1e51e5 to 1.5e51.5e5 to 2e5>= 2e5

6.358.4611.411.411.512.916.213.14.284.38

Gender

MaleFemale

48.351.7

1.52 ± 0.5

Children ages 2-5

01

85.114.9

0.15 ± 0.36

Children under age 2

01

90.29.82

0.1 ± 0.3

Children ages 18-up

01

79.420.6

0.21 ± 0.4

Age

13 to 1717 to 2424 to 3434 to 3939 to 4444 to 4949 to 5454 to 5959 to 64>= 64

0.7710.428.114.713.311.99.795.382.982.77

Demographic Bayes NetCPTs learned from 1.5M cases in the file

A. Darwiche

A Bayesian NetworkA Bayesian Network

• Compact representation of a probability distribution:– Complete model– Consistent model

• Embeds many independence assumptions:– Faithful model

A. Darwiche

A. Darwiche

A Bayesian NetworkA Bayesian Network

• Compact representation of a probability distribution:– Complete model– Consistent model

• Embeds many independence assumptions:– Faithful model

A. Darwiche

Bayesian NetworkBayesian Network

Earthquake (E) Burglary (B)

Alarm (A)

Pr(E=true) Pr(E=false)

.1 .9

Pr(B=true) Pr(B=false)

.2 .8

Pr(A=true) Pr(A=false)

E=true, B=true.95 .05

E=false, B=true.9 .1

E=true, B=false.7 .3

E=false, B=false.01 .99

A. Darwiche

Joint Probability DistributionJoint Probability DistributionE B A Pr(.)

True True True .019

True True False .001

True False True .056

True False False .024

False True True .162

False True False .018

False False True .0072

False False False .7128

A. Darwiche

Independence AssumptionsIndependence Assumptionsof a Bayesian Networkof a Bayesian Network

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Chol

Test1 Test2

Causal StructureCausal Structure

I(Test1,Test2 | Chol)

A. Darwiche

Chol

Test1 Test2

Causal StructureCausal Structure

Nurse

I(Test1,Test2 | Chol, Nurse)

I(Test1,Test2 | Chol)

A. Darwiche

H

O1 On

Naïve BayesNaïve Bayes

O2

H: DiseaseO1, …, On: Findings (symptoms, lab tests, …)

…

A. Darwiche

Genetic TrackingGenetic Tracking

G1 G2

G3 G4G5

G6 G7 G8 P4

Each node is independent of its non-descendants given its parents

A. Darwiche

Dynamic SystemsDynamic Systems

S1

O1

S2

O2

S3

O3

S4

O4

S5

O5

Each node is independent of its non-descendants given its parents

A. Darwiche

The chain rule for The chain rule for Bayesian NetworksBayesian Networks

A. Darwiche

Example: Build Joint Probability Example: Build Joint Probability TableTable


Alarm (A)

Pr(E=true) Pr(E=false)

.1 .9

Pr(B=true) Pr(B=false)

.2 .8

Pr(A=true) Pr(A=false)

E=true, B=true.95 .05

E=false, B=true.9 .1

E=true, B=false.7 .3

E=false, B=false.01 .99

A. Darwiche

Temperature/SensorsTemperature/Sensors

• Temperature: high (20%), low (10%), nominal (70%)

• 3 Sensors (true, false):true (90%) given high temperaturetrue (1%) given low temperaturetrue (5%) given nominal temperature

A. Darwiche

A. Darwiche

QueriesQueries

• Pr(Sensor1=true)?

• Pr(Temperature=high | Sensor1=true)?

• Pr(Temperature=high | Sensor1=true,Sensor2=true, Sensor3=true)?

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d-separationd-separation

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

… (F)

Is A Independent of R given E?

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Chain LinkE & C not d-separated

…Active!

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Chain LinkE & C are d-separated by A

…Blocked!

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Divergent LinkR & A not d-seperated

…Active!

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Divergent LinkR & A d-separated by E

…Blocked!

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Convergent LinkE & B d-seperated

…Blocked!

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Convergent LinkE & B not d-separated by A

…Active!

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Convergent LinkE & B not d-separated by C

…Active!

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Are B & R d-separated by E & C ?

ActiveBlocked

A. Darwiche


Alarm (A)

Call (C)

Radio (R)

Active

Active

Are C & R d-separated ?

A. Darwiche

blocked

blocked

active

A. Darwiche

d-separationd-separation

• Nodes X are d-separated from nodes Y by nodes Z iff every path from X to Y isblocked by Z.

• A path is blocked by Z if some link on the path is blocked:– For some →X→ or ←X→, X in Z

– For some →X←, neither X nor one of its descendents in Z

A. Darwiche

d-separation in Asia Networkd-separation in Asia Network

• Visit to Asia / Smoker:– No evidence: No– Given TB-or-Cancer: Yes– Given +ve X-Ray: Yes

• Visit to Asia / +ve X-ray:– No evidence: Yes– Given TB: No– Given TB-or-Cancer: No

• Bronchitis / Lung Cancer:– No evidence: Yes– Given Smoker: No– Given Smoker and Dysnpnoea: Yes

a. darwiche bayesian networks. a. darwiche bayesian network battery age alternator fan belt battery...

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darwiche slide

bayesian network slide

false e

test2 chol slide

faithful model slide

nominal temperature

darwiche example

darwiche bayesian networks