laskey - medg 1 multi-entity decision graphs: a graphical modeling language kathryn blackmond laskey...

Laskey - MEDG 1

Multi-Entity Decision Graphs:A Graphical Modeling Language

Kathryn Blackmond LaskeyGeorge Mason University

[email protected]

February, 2002February, 2002

Laskey - MEDG 2

[Security experts] pointed out [Security experts] pointed out that the linchpin of the system that the linchpin of the system

is not Jersey barriers and metal is not Jersey barriers and metal detectors, but intelligence that detectors, but intelligence that

a threat may be coming.a threat may be coming.Washington Post, September 12, 2001Washington Post, September 12, 2001

[Security experts] pointed out [Security experts] pointed out that the linchpin of the system that the linchpin of the system

is not Jersey barriers and metal is not Jersey barriers and metal detectors, but intelligence that detectors, but intelligence that

a threat may be coming.a threat may be coming.Washington Post, September 12, 2001Washington Post, September 12, 2001

This presentation is dedicated to the memory of journalist Danny Pearl, brutally This presentation is dedicated to the memory of journalist Danny Pearl, brutally murdered in Pakistan in February 2002, and to the pioneering research of his father murdered in Pakistan in February 2002, and to the pioneering research of his father

Judea Pearl, which will enable unprecedented leaps in decision support technology that Judea Pearl, which will enable unprecedented leaps in decision support technology that could anticipate and prevent future terrorist incidents.could anticipate and prevent future terrorist incidents.

Laskey - MEDG 3

Requirements for Inference

and Decision Support• Support not replace the human

• Extract relevant conclusions from huge volumes of data

• Detect anomalous configurations of indicators that appear minor when taken individually

• Respond rapidly to unanticipated situations

• Cope with uncertainty and ambiguity

• Support top-down control of– Allocation of computational resources

– Choice of information to display and format of display

– Management of collection resources

Laskey - MEDG 4

Example: An Evolving Situation

• Maria is visiting a friend when she Maria is visiting a friend when she suddenly begins sneezing. suddenly begins sneezing.

• "Oh dear, I'm getting a cold," she "Oh dear, I'm getting a cold," she thinks. “I had better not visit Grandma.”thinks. “I had better not visit Grandma.”

• Then she notices scratches on the Then she notices scratches on the furniture. She sighs in relief. "I'm not furniture. She sighs in relief. "I'm not getting a cold! It's only my cat allergy getting a cold! It's only my cat allergy acting up!”acting up!”

• Maria is visiting a friend when she Maria is visiting a friend when she suddenly begins sneezing. suddenly begins sneezing.

• "Oh dear, I'm getting a cold," she "Oh dear, I'm getting a cold," she thinks. “I had better not visit Grandma.”thinks. “I had better not visit Grandma.”

• Then she notices scratches on the Then she notices scratches on the furniture. She sighs in relief. "I'm not furniture. She sighs in relief. "I'm not getting a cold! It's only my cat allergy getting a cold! It's only my cat allergy acting up!”acting up!”

Allergic_Reaction

TrueFalse

3.2296.8

Sneezing

TrueFalse

15.384.7

Scratches_on_Furniture

TrueFalse

2.7797.2

Cold

TrueFalse

8.0092.0

Cat_Nearby

TrueFalse

3.0097.0

HealthOfGrandmother

VisitGrandmother

GoStayHome

117.000100.000

Pleasure

Allergic_Reaction

TrueFalse

3.2296.8

Sneezing

TrueFalse

15.384.7


TrueFalse

2.7797.2

Cold

TrueFalse

8.0092.0

Cat_Nearby

TrueFalse

3.0097.0

HealthOfGrandmother

VisitGrandmother

GoStayHome

117.000100.000

Pleasure

11

Plausible inferencePlausible inference

Allergic_Reaction

TrueFalse

20.879.2

Sneezing

TrueFalse

100 0


TrueFalse

9.9590.1

Cold

TrueFalse

51.748.3

Cat_Nearby

TrueFalse

15.284.8

HealthOfGrandmother

VisitGrandmother

GoStayHome

73.2510100.000

Pleasure

Allergic_Reaction

TrueFalse

20.879.2

Sneezing

TrueFalse

100 0


TrueFalse

9.9590.1

Cold

TrueFalse

51.748.3

Cat_Nearby

TrueFalse

15.284.8

HealthOfGrandmother

VisitGrandmother

GoStayHome

73.2510100.000

Pleasure

22

The evidence for cat allergy The evidence for cat allergy ““explains away” your sneezingexplains away” your sneezingand cold is no longer needed and cold is no longer needed

as an explanationas an explanation

Allergic_Reaction

TrueFalse

88.411.6

Sneezing

TrueFalse

100 0


TrueFalse

100 0

Cold

TrueFalse

14.485.6

Cat_Nearby

TrueFalse

91.58.53

HealthOfGrandmother

VisitGrandmother

GoStayHome

110.592100.000

Pleasure

Allergic_Reaction

TrueFalse

88.411.6

Sneezing

TrueFalse

100 0


TrueFalse

100 0

Cold

TrueFalse

14.485.6

Cat_Nearby

TrueFalse

91.58.53

HealthOfGrandmother

VisitGrandmother

GoStayHome

110.592100.000

Pleasure

33

Laskey - MEDG 5

Decision Graphs

• Both a knowledge representation and a computational architecture

– Represents knowledge about variables and their interactions– Modular elements with defined interconnections– Computation can exploit loosely coupled structure for efficiency

• Standard software & theory limited to “template models”

– All problem instances involve:» Same set of variables» Same states for variables» Same relationships between variables

– Same decision graph can be used for all problem instances– Only “evidence” (instantiated variables) varies from instance to

instance– All potentially relevant explanations are explicitly represented

Laskey - MEDG 6

Technology Gap

• In complex, open-world problems:– Number of actors and relationships to each other not fixed in

advance– Attribution of evidence to actors may not be known in advance– Situation evolves in time– Need to represent only the most important explanations

• Why there is hope– Actors of given type have similar features & behavior– Relevant variables & relationships depend on type of actor

• Can we capture the regularities and retain open-world flexibility?

Laskey - MEDG 7

Maria’s Continuing Saga…

• Variation 1:– Tran is sneezing and saw scratches

– Tran was recently exposed to a cold and probably is not allergy prone

• Variation 2:– Tran saw scratches

– Maria did not see scratches

– Tran is in room with Maria

• Variation 3:– Tran and Maria both are sneezing, are allergy prone, and

saw scratches

– Tran and Maria are a continent apart

Laskey - MEDG 8

Variation 1

AllergyProne(Maria)

TrueFalse

100 0

AllergicReaction(Mar ...

TrueFalse

88.211.8

Sneezing(Maria)

TrueFalse

100 0

SeesScratches(Mar...

TrueFalse

100 0

ExposedToCold(Maria)

TrueFalse

15.784.3

ColdStatus(Maria)

TrueFalse

15.085.0

NearCat(Maria)

TrueFalse

91.48.63

Health(Grandmother1)

Pleasure(Maria,Grandmother1)Visit(Maria,Grandmother1)

GoStayHome

109.977100.000

AllergyProne(Maria)

TrueFalse

100 0


TrueFalse

88.211.8

Sneezing(Maria)

TrueFalse

100 0


TrueFalse

100 0


TrueFalse

15.784.3

ColdStatus(Maria)

TrueFalse

15.085.0

NearCat(Maria)

TrueFalse

91.48.63


Pleasure(Maria,Grandmother1)Visit(Maria,Grandmother1)

GoStayHome

109.977100.000

Allergy_Prone(Tran)

TrueFalse

5.7194.3

Allergic_Reaction(Tran)

TrueFalse

4.4395.6

Sees_Scratches(Tran)

TrueFalse

100 0

Cold_Status(Tran)

TrueFalse

97.32.69

Exposed_to_Cold(Tran)

TrueFalse

100 0

Near_Cat(Tran)

TrueFalse

65.534.5

Sneezing(Tran)

TrueFalse

100 0

Visit(Tran,Grandmother2)

GoStayHome

27.6902100.000


Pleasure(Tran,Grandmother2)

Allergy_Prone(Tran)

TrueFalse

5.7194.3

Allergic_Reaction(Tran)

TrueFalse

4.4395.6


TrueFalse

100 0

Cold_Status(Tran)

TrueFalse

97.32.69

Exposed_to_Cold(Tran)

TrueFalse

100 0

Near_Cat(Tran)

TrueFalse

65.534.5

Sneezing(Tran)

TrueFalse

100 0

Visit(Tran,Grandmother2)

GoStayHome

27.6902100.000


Pleasure(Tran,Grandmother2)

• Add background variables to specialize model to different individuals

• Still a “template model” with limited expressive power

Laskey - MEDG 9

Variation 2

• Decision graph has replicated sub-parts

• Different kinds of entities (cats and people)


TrueFalse

54.945.1

AllergicReaction(Tran)

TrueFalse

5.6694.3

ColdStatus(Tran)

TrueFalse

97.02.98

Sneezing(Tran)

TrueFalse

100 0

AllergyProne(Maria)

TrueFalse

100 0


TrueFalse

88.111.9

Sneezing(Maria)

TrueFalse

100 0


TrueFalse

15.884.2

ColdStatus(Maria)

TrueFalse

15.085.0

Near(Tran,Cat1)

TrueFalse

91.48.59

Near(Maria,Cat1)

TrueFalse

91.38.68


TrueFalse

100 0

AllergyProne(Tran)

TrueFalse

5.9994.0

ExposedToCold(Tran)

TrueFalse

100 0

Loc(Tran) Loc(Maria)Loc(Cat1)

Near(Maria,Tran)

TrueFalse

100 0

Health(Grandmother,T1)

Pleasure(Maria,Grandmother,T1)Visit(Maria,Grandmother, ...

GoStayHome

109.950100.000


TrueFalse

54.945.1


TrueFalse

5.6694.3

ColdStatus(Tran)

TrueFalse

97.02.98

Sneezing(Tran)

TrueFalse

100 0

AllergyProne(Maria)

TrueFalse

100 0


TrueFalse

88.111.9

Sneezing(Maria)

TrueFalse

100 0


TrueFalse

15.884.2

ColdStatus(Maria)

TrueFalse

15.085.0

Near(Tran,Cat1)

TrueFalse

91.48.59

Near(Maria,Cat1)

TrueFalse

91.38.68


TrueFalse

100 0

AllergyProne(Tran)

TrueFalse

5.9994.0

ExposedToCold(Tran)

TrueFalse

100 0


Near(Maria,Tran)

TrueFalse

100 0



GoStayHome

109.950100.000

Laskey - MEDG 10

Variation 3 Done Wrong

• Version 2 model gets wrong answer if Maria and Tran are not near each other and both are near cats!

• We need to be able to hypothesize additional cats if and when necessary


TrueFalse

100 0


TrueFalse

51.049.0

ColdStatus(Tran)

TrueFalse

35.964.1

Sneezing(Tran)

TrueFalse

100 0

AllergyProne(Maria)

TrueFalse

100 0


TrueFalse

51.049.0

Sneezing(Maria)

TrueFalse

100 0


TrueFalse

33.866.2

ColdStatus(Maria)

TrueFalse

35.964.1

Near(Tran,Cat1)

TrueFalse

49.550.5

Near(Maria,Cat1)

TrueFalse

49.550.5


TrueFalse

100 0

AllergyProne(Tran)

TrueFalse

100 0

ExposedToCold(Tran)

TrueFalse

33.866.2


Near(Maria,Tran)

TrueFalse

0 100



GoStayHome

89.1446100.000


TrueFalse

100 0


TrueFalse

51.049.0

ColdStatus(Tran)

TrueFalse

35.964.1

Sneezing(Tran)

TrueFalse

100 0

AllergyProne(Maria)

TrueFalse

100 0


TrueFalse

51.049.0

Sneezing(Maria)

TrueFalse

100 0


TrueFalse

33.866.2

ColdStatus(Maria)

TrueFalse

35.964.1

Near(Tran,Cat1)

TrueFalse

49.550.5

Near(Maria,Cat1)

TrueFalse

49.550.5


TrueFalse

100 0

AllergyProne(Tran)

TrueFalse

100 0

ExposedToCold(Tran)

TrueFalse

33.866.2


Near(Maria,Tran)

TrueFalse

0 100



GoStayHome

89.1446100.000

Laskey - MEDG 11

Variation 3 Done Right(…but what a mess!)

• This model gets the right answer on all the variations

Loc(Cat2,T1)

Near(Maria,Cat2,T1)

TrueFalse

42.957.1

AllergyProne(Maria)

TrueFalse

100 0

AllergicReaction(Maria, ...

TrueFalse

82.817.2

Sneezing(Maria,T1)

TrueFalse

100 0

SeesScratches(Maria, ...

TrueFalse

100 0

Sneezing(Tran,T1)

TrueFalse

100 0

AllergyProne(Tran)

TrueFalse

100 0

AllergicReaction(Tran,T1)

TrueFalse

82.817.2

SeesScratches(Tran, ...

TrueFalse

100 0

Near(Maria,{c}:Cat,T1)

TrueFalse

85.314.7

Near(Maria,Cat1:Cat, ...

TrueFalse

42.757.3


TrueFalse

42.757.3

Type(Cat1)

CatOther

92.27.77

Near(Tran,Cat1:Cat,T1)

TrueFalse

42.757.3

Near(Tran,{c}:Cat,T1)

TrueFalse

85.314.7


TrueFalse

42.757.3

Type(Cat2)

CatOther

92.27.77

Near(Tran,Cat1,T1)

TrueFalse

42.957.1

Near(Maria,Cat1,T1)

TrueFalse

42.957.1

Near(Maria,Tran,T1)

TrueFalse

0 100

Near(Tran,Cat2,T1)

TrueFalse

42.957.1

Loc(Cat1,T1)

Loc(Tran,T1) Loc(Maria,T1)

ColdStatus(Tran,T0)

ColdExposedHealthy

13.813.073.2

ColdStatus(Tran,T1)

ColdExposedHealthy

18.08.7973.2

ColdStatus(Maria,T1)

ColdExposedHealthy

18.08.7973.2


ColdExposedHealthy

13.813.073.2

Visit(Maria,Grandmother, ...

GoStayHome

107.03399.9999

Pleasure(Maria,Grandmother,T1)


Loc(Cat2,T1)

Near(Maria,Cat2,T1)

TrueFalse

42.957.1

AllergyProne(Maria)

TrueFalse

100 0

AllergicReaction(Maria, ...

TrueFalse

82.817.2

Sneezing(Maria,T1)

TrueFalse

100 0

SeesScratches(Maria, ...

TrueFalse

100 0

Sneezing(Tran,T1)

TrueFalse

100 0

AllergyProne(Tran)

TrueFalse

100 0

AllergicReaction(Tran,T1)

TrueFalse

82.817.2

SeesScratches(Tran, ...

TrueFalse

100 0

Near(Maria,{c}:Cat,T1)

TrueFalse

85.314.7


TrueFalse

42.757.3


TrueFalse

42.757.3

Type(Cat1)

CatOther

92.27.77


TrueFalse

42.757.3

Near(Tran,{c}:Cat,T1)

TrueFalse

85.314.7


TrueFalse

42.757.3

Type(Cat2)

CatOther

92.27.77

Near(Tran,Cat1,T1)

TrueFalse

42.957.1

Near(Maria,Cat1,T1)

TrueFalse

42.957.1

Near(Maria,Tran,T1)

TrueFalse

0 100

Near(Tran,Cat2,T1)

TrueFalse

42.957.1

Loc(Cat1,T1)

Loc(Tran,T1) Loc(Maria,T1)

ColdStatus(Tran,T0)

ColdExposedHealthy

13.813.073.2

ColdStatus(Tran,T1)

ColdExposedHealthy

18.08.7973.2


ColdExposedHealthy

18.08.7973.2


ColdExposedHealthy

13.813.073.2

Visit(Maria,Grandmother, ...

GoStayHome

107.03399.9999

Pleasure(Maria,Grandmother,T1)


Laskey - MEDG 12

ColdStatus(h1,t)

ColdExposedHealthy

8.359.8281.8

Visit(h1,h2,t)

GoStayHome

116.651100.000

Health(h2,t)

Pleasure(h1,h2,t)

ColdStatus(h1,t)

ColdExposedHealthy

8.359.8281.8

Visit(h1,h2,t)

GoStayHome

116.651100.000

Health(h2,t)

Pleasure(h1,h2,t)

The Solution

SeesScratches(h,t)

TrueFalse

2.6397.4

Near(h,:Cat,t)

TrueFalse

2.7697.2

AllergicReaction(h,t)

TrueFalse

1.1098.9

AllergyProne(h)

TrueFalse

5.0095.0

SeesScratches(h,t)

TrueFalse

2.6397.4

Near(h,:Cat,t)

TrueFalse

2.7697.2


TrueFalse

1.1098.9

AllergyProne(h)

TrueFalse

5.0095.0

Loc(y,t)

Near(x,y,t)

TrueFalse

3.0497.0

Loc(x,t)Loc(y,t)

Near(x,y,t)

TrueFalse

3.0497.0

Loc(x,t)

Type(c)

CatOther

50.050.0

Near(x,c:Cat,t)

TrueFalse

1.5098.5

Near(x,{c}:Cat,t)

TrueFalse

2.4897.5

Near(x,c,t)

TrueFalse

3.0097.0

Type(c)

CatOther

50.050.0

Near(x,c:Cat,t)

TrueFalse

1.5098.5

Near(x,{c}:Cat,t)

TrueFalse

2.4897.5

Near(x,c,t)

TrueFalse

3.0097.0

Sneezing(h,t)

TrueFalse

17.282.8


TrueFalse

1.1398.9

ColdStatus(h,t)

ColdExposedHealthy

12.0 0

88.0

Sneezing(h,t)

TrueFalse

17.282.8


TrueFalse

1.1398.9

ColdStatus(h,t)

ColdExposedHealthy

12.0 0

88.0

ColdStatus(h,t-1)

ColdExposedHealthy

8.359.8281.8

ColdStatus(h,t)

ColdExposedHealthy

8.359.8281.8

ColdStatus(h,t-1)

ColdExposedHealthy

8.359.8281.8

ColdStatus(h,t)

ColdExposedHealthy

8.359.8281.8

Cats & AllergiesCats & AllergiesFragmentFragment

SpatialSpatialFragmentFragment

HypothesisHypothesisManagementManagement

FragmentFragment

Colds&Time Colds&Time FragmentFragment

ValueValueFragmentFragment

SneezingSneezingFragmentFragment

• Specify model in pieces and let the computer compose them

Laskey - MEDG 13

Multi-Entity Decision Graphs

• Represent knowledge as model fragments– Implicitly represents complete and consistent model of domain and

anticipated situations– No a priori bound on #entities, #relevant relationships, #observations

• Compose fragments dynamically into situation specific network (SSN)

– A situation is a snapshot of the world at an instant of time– A situation-specific network is an ordinary, finite Bayesian network or

decision graph constructed from the MEDG knowledge base using network construction operators

• Use SSN to compute response to query – Approximates the “correct answer” encoded by the knowledge base

• Use expert-guided Bayesian learning to update knowledge patterns over time

Laskey - MEDG 14

Model Construction

• Simpler models give same results as more complex model on problems for which they are adequate

• We want to construct “good enough” model for our situation

• Model constructor builds situation-specific DG from knowledge base implicitly encoding infinite-dimensional DG

Laskey - MEDG 15

Models

• Our real goal is to find the action that maximizes E[Utility(Consequence)|Action)]

• We don't know E[Utility(Consequence)|Action)]

• We construct a model M (decision theoretic or not) which is a recipe for selecting an action

• We hope M is a good representation of the problem and will get us close to our optimal expected utility

• For a decision theoretic model this means: – E[Utility(Consequence)|Action,M)] ≈ E[Utility(Consequence)|Action)]

All models are wrong but some are usefulAll models are wrong but some are usefulAll models are wrong but some are usefulAll models are wrong but some are useful

Laskey - MEDG 16

Savage and the “Problem of Small Worlds”

• L. J. Savage on the problem of small worlds– "A person has only one decision to make in his life. He must … decide how to live."

– "[There is a] practical necessity of confining attention … to relatively simple situations…"

– "I find it difficult to say with any completeness how such isolated situations are actually arrived at and justified."

• What happens when you make your small world too small?– Capturing that inviting rook gives your opponent the opportunity for checkmate

– Actions intended to increase standard of living lead to pollution and global warming

– Actions intended to improve world health (large-scale use of antibiotics) lead to disease-resistant bacteria and overpopulation

• MEDGs solve the problem of small worlds– “Grand world” model is specified implicitly via “small world” models plus conditional

exchangeability assumptions

– SSN construction can be formulated as a decision problem

– Model tradeoff between tractability and problem utility

– Theoretical optimum SSN construction and evidence propagation algorithm exists for any class of problems

– Practical engineering problem: approximate theoretical optimum

Laskey - MEDG 17

MEDGs andObject-Oriented Representation

• Entities of MEDG can be modeled as objects– Organized in type/subtype hierarchy– Similar behavior and structure across types– Can be composed of other entities– Can be related to other entities

» Inheritance, composition, association

• Probability part of MEDG expresses uncertainty about attributes of entities, composition of entities, and their associations

• Value and action part of MEDG represents objectives and plans of software agent

MammalMammal

PhysicalPhysicalObjectObject

HumanHuman CatCat

LocationLocation TimeTime




NearNear

InheritanceInheritance AssociationAssociation

CompositionComposition

Laskey - MEDG 18

Speculations on the Future

• 20th century physics replaced traditional deterministic dynamics with explicitly probabilistic dynamics

– Uncertainty is an intrinsic, irreducible element of present-day physics– Most non-physical scientists were trained in classical deterministic physics and

are not fully aware of the implications of quantum mechanics– This has influenced the way in which researchers have attempted to model the

natural world– This has also influenced our approach to computing and the development of

intelligent systems• Speculation: 21st century computing will replace deterministic

computing dynamics with probabilistic “physical symbol system” dynamics

– Old paradigm:» Deterministic steps transform inputs into outputs» Result is either right or wrong» Semantics based on Boolean logic

– New paradigm» Stochastic steps transform inputs into sequence of trial solutions» “Program” is replaced by dynamic system in which solution quality improves over time» Semantics based on decision theory

– Old paradigm model is limiting case of new paradigm

Laskey - MEDG 19

Physical Symbol Systemsand 21st Century Computing

• Physical symbol system (Newell and Simon)– Contains physical entities that serve as symbols

– Symbols can designate entities in the world

– System can interpret symbol structures to alter its behavior in a way that depends on designated entities

• Recent trend in optimization and learning: – Construct fictitious physical system in which measure of

solution quality maps onto action (or free energy or energy)

– Apply solution methods imported from computational physics

– This works because physical systems minimize action

• Suggested 21st century computing paradigm– Implement MEDG (or similar) logic in quantum hardware

– Replace “programming” with “goal setting” and let system find the best way to evolve to high-quality solution

Laskey - MEDG 20

Summary

• MEDGs move Bayesian Network and influence diagram technology from hand-crafted special purpose models to genuine open-world reasoning capability

• Knowledge base of modular elements is combined at run time to construct problem-specific model

• MEDGs provide an answer to Savage’s “problem of small worlds”

• MEDGs may lead to a new logic for computing

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