ben gal

“To Explain or To Predict”

“To Know or To Act” (Pure Science vs. Engineering, 2004)

Using Target-Based Bayesian Nets for Suspects Monitoring (joint work with A. Gruber and S. Yanovski)

Irad Ben-Gal

Tel Aviv University

Tel Aviv University Department of Industrial Engineering

DOE: Vs-optimal designs Ginsburg & Ben-Gal (2004)

f(x) known: f(x)/x=0 x*

f(x) unknown:

Estimate g(x) (Meta Model: DOE, RSM,…)

g(x)/x=0 x* (R.V.)

‘Scientists’ (to Know): Best estimation of f(x) min V() (e.g., D-optimal exp.)

‘Practitioner’ (to act) : Best estimation of x* min V(x*) (new DOE optimality criterion)

f(x) x (control) Y (output)


The Bias-Variance Tradeoff


Presentation Layout

Bayesian networks and classifiers

Targeted Bayesian Network Learning (TBNL) (with Gruber)

TBNL application on suspects monitoring

Summary

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Bayesian Networks (Pearl, 85)


What is a Bayesian Network?

X1 X2 X3 X4 Prob.

1 1 1 2 0.083

1 1 2 2 0.167

1 2 2 3 0.25

2 2 1 1 0.25

2 2 2 1 0.25

Joint Probability

Distribution

),,|(),|()|()()(2341234232

XXXXPXXXPXXPXPP X

A Complete

Bayesian Network

encodes the domain’s JPD ),( ΘGB

EV ,G = Directed Acyclic Graph

X2 1 2

1 0.33 0.33

2 0.67 0.67

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)(3

XΘ

Factorization


Explain or Predict (classify)

Tree / GBN Chow & Liu (1968)

Williamson (2000) TBNL

Gruber & Ben-Gal (2010)

True distribution

Modeled distribution

Objective

Principle Minimize Minimize

Consequence

Maximize

Maximize

Maximize

)( Xp

)( Xq

)( Xp

XX qpD ||KL

i

iiZXI ;

)( Xp

)( Xq

ii

XqXpD ||KL

ii

ZXI ;

ijZX

jjZXI ;

''|

\'

xx

Xx

pXpXp

iX

ii

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Unconstrained Learning

GBN (adding-arrows) Target-Oriented (TBNL)

Assume is the target variable 3

X

i=1 i=4 i=3 i=1 i=4

Equivalent Encoding!!!

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Constrained Learning

Assume is the target variable 3

X

i=1 i=4 i=1 i=4 i=3

GBN (adding-arrows) Target-Oriented (TBNL)

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Differential Complexity

r t

𝜂𝑡 = maximum percentage relative information exploitation about the target

𝜂𝑟 = maximum percentage relative information exploitation about the rest attributes

Predict (Classify)

Explain


Results (1/2) Data Sets Properties and Testing Methods

Dataset # Attributes # Classes # Instances Test Instances/Attributes Ratio

australian 14 2 690 CV5 ~49

breast 9 2 683 CV5 ~76

chess 36 2 3196 holdout ~89

cleve 11 2 196 CV5 ~18

corral 6 2 128 CV5 ~21

crx 15 2 653 CV5 ~44

german 20 2 1000 CV5 ~50

glass 9 7 214 CV5 ~24

Iris 5 3 150 CV5 ~30

lymphography 18 4 148 CV5 ~8

mofn-3-7-10 10 2 1324 holdout ~132

vote 16 3 435 CV5 ~27

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Naïve Bayes: Predict

A0

A1

B0

B1Irrelevant

Correlated

Class

Corral Dataset

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A0A1

B0

B1 Irrelevant

Correlated

Class

A0

A1

B0

B1

Irrelevant

Correlated

Class

A0

A1

B0

B1

Irrelevant

Correlated

Class

A0

A1

B0

B1

Irrelevant

Correlated

Class

Tree Augmented Network (TAN)

A0

A1

B0

B1

Irrelevant

Correlated

Class

A0

A1

B0 B1

Irrelevant

Correlated

Class

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Managing the Trade-off

CV5

CV5

Holdout

2/3:1/3

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Results (2/2) Accuracy

Best & worst methods (incl. 5% runner up) in Bold & Italic respectively

Dataset TBNL BNC-2P NB TAN C4.5 HGC

australian 83.3 87.0 85.1 82.5 84.9 85.6

breast 95.9 95.8 97.6 96.5 93.9 97.6

chess 96.9 95.8 87.3 92.4 99.5 95.3

cleve 81.4 80.0 82.1 78.4 79.4 78.7

corral 100.0 98.8 87.2 98.6 98.5 100.0

crx 86.4 84.2 85.0 83.7 86.1 86.9

german 69.7 73.6 75.4 73.9 72.9 72.5

glass 60.0 58.3 55.9 54.2 59.3 31.2

Iris 97.0 95.8 93.0 92.4 96.0 95.7

lymphography 81.8 83.7 83.4 82.2 78.4 63.8

mofn-3-7-10 100.0 91.4 86.7 91.5 84.0 86.7

vote 96.0 95.8 90.1 94.9 94.7 95.4

Average 87.4 86.7 84.1 85.1 85.6 82.4

StdE 4% 3% 3% 4% 3% 6%

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Paired t-tests show significance


Presentation Layout

Bayesian networks and classifiers

Targeted Bayesian Network Learning (TBNL)

TBNL application on suspects monitoring (w. Gruber & Yanovski)

Summary

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Domain Description

Motivation Simplicity: complexity-error tradeoff

Information extraction: utilization of meta-data

Support: help the expert understand

Available Data CDR

Privatized

Laundered

Requirements 50% Recall with 1% False Alarm at most

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Data Description of the Domain

Field Description

Main party Monitored Object unique IDENTIFIER

Other party Other Party unique IDENTIFIER

year Year of call start

month Month of call start

day Day of call start

hour Hour of call start

minute Minute of call start

second Second of call start

duration Call duration in Seconds

caller Indication of call initiator : {1/0}

1 – main party initiated the call

0 – other party initiated the call

type_id Type of interaction initiator : {1/0}

1 - phone call

0 - sms (text message)

tag Type (group) of monitored Object : {1/0}

0 – main party is a non-target

1 – main party is a target

Call Detail Record (CDR)

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ROC curve

1900

missed

targets

40 suspects to no avail

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Feature Extraction

Inter_prc_q1, Inter_prc_q2, Inter_prc_q3, Inter_prc_q4 – percentage of

activities in 1st, 2nd, 3rd and 4th quarter of the day

Activity of calls during the day of two distinct groups

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Learning & Mining Mobility Patterns (PI’s: Ben-Gal, Toch and Lerner, 2012)


Conclusions

“To Explain or to Predict” –

“To know or to Act” (constraint modeling)

Managing the error-complexity tradeoff!

An “engineering approach” to modeling

Target-based BN Learning (2006), Gruber and Ben-Gal (2010)…

Vs-optimality criterion min V(x*), Ginsburg and Ben-Gal (2006)

VOBN Ben-Gal et at (2005) – scenario dependent

More….

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Prediction can help…

ben gal

Technology

p x q x

x p x objective

maximizei x

best estimation of x

p xi q x

gruber tbnl application

bayesian networks pearl

targetbased bayesian