Uncertainty in Probabilistic Trust Models

In the Name of AllahIn the Name of Allah

Data and Network Data and Network Security Lab. (DNSL)Security Lab. (DNSL)

Sharif UniversitySharif Universityof Technologyof Technology Security Lab. (DNSL)Security Lab. (DNSL)of Technologyof Technology

Sadegh Dorri Nogoorani, Rasool Jalili

Uncertainty in Probabilistic Trust ModelsUncertainty in Probabilistic Trust Models

The 26th IEEE Int. Conf. Advanced Information Networking and Applications (AINA 2012)

Sharif University of Technology, Tehran, I.R. IRAN

http://ce.sharif.edu/~dorri

Who Knows on the Net...?Who Knows on the Net...?

A notion of trust similar to A notion of trust similar to real world trust is real world trust is

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real world trust is real world trust is needed in the virtual needed in the virtual world…world…

Coordinating Agent Coordinating Agent Interactions without Interactions without Strict Control Strict Control MechanismsMechanismsMechanismsMechanisms

Fig. by Peter Steiner (The New Yorker, 5 July 1993)Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012

Uncertainty and TrustUncertainty and Trust

Uncertainty = Lack of InformationUncertainty = Lack of Information

Randomness, fuzziness, vagueness, ambiguity

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Randomness, fuzziness, vagueness, ambiguity

Modeling of UncertaintyModeling of Uncertainty

Probability: a long history, suited to random events

Fuzzy sets: since 1960s, suitable for human interaction

Dempster-Shafer theory: since 1970s, based on beliefs

Uncertainty in TrustUncertainty in Trust

Uncertainty of information (error, human feedback, …) Uncertainty of information (error, human feedback, …)

Expiration of information: change in trustee behavior

Credibility of trust information: recommendations, path length

Trust modes: induction, abstraction, …

Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012

OutlineOutline

BackgroundBackground

Probabilistic trust framework

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Probabilistic trust framework

Case StudyCase Study

Uncertainty in two prob. trust models

A ProposalA Proposal

Uncertainty-driven risk reduction with trust Uncertainty-driven risk reduction with trust

Future WorkFuture Work

Other forms of uncertainty


BackgroundBackground5

Probabilistic Trust FrameworkProbabilistic Trust Framework

BackgroundBackground5


Trust ScenarioTrust Scenario

Direct Trust

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Trustor Trustee

Direct Trust

Functional

Referential Functional

Functional

Indirect Trust (Inference)

Referential Functional

RecommendersUncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012

Probabilistic Trust FrameworkProbabilistic Trust Framework

Definition of Trust (Adopted from [GamDefinition of Trust (Adopted from [Gam9090]):]):

The subjective probability by which trustor expects that

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The subjective probability by which trustor expects that trustee performs a given action, on which its welfare depends.

Trust: The (Expected) Probability of Positive OutcomeTrust: The (Expected) Probability of Positive Outcome

Action outcome:

Probability of success

Trust (Bayesian view)

, xxR =),,|Pr( ,,

1,, tetr

tntetr

ttetr

ttetr

t OOxOp …==][ ,, tetrtetr pE=τ Trust (Bayesian view)

From now on, a specific From now on, a specific trtr, , tete, and , and tt are implicitly are implicitly assumed.assumed.

][ ,, tetrt

tetrt pE=τ


The Beta Trust Model [JIThe Beta Trust Model [JI0202]]

Outcomes Assumed to be Bernoulli Trials (Outcomes Assumed to be Bernoulli Trials (i.i.di.i.d.).) =

==xop

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Hence, Hence, pp Follows the Beta DistributionFollows the Beta Distribution

r: success outcomes

s: failure outcomes

Trust 1]E[

+== rpτ

=−=

==xop

xopoO

1)Pr(

sr ppsr

srpf )1(

)1()1(

)2()( −

+Γ+Γ++Γ=

Trust

Change of Trustee BehaviorChange of Trustee Behavior

Forgetting facotr (λ)

2]E[

++==

srpτ

)(

)(

)1(

)1(

tnxnttn

tnxnttn

OIss

OIrr

+=

+=

−

−

λλ


The HMM Trust Model [ESNThe HMM Trust Model [ESN1010]]

Trustee Is Modeled with a Trustee Is Modeled with a 22--State Hidden Markov Model State Hidden Markov Model (HMM) (HMM) –– ΩΩ

2 (hidden) states (benevolent/malicious)

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2 (hidden) states (benevolent/malicious)

2 possible outputs with independent Bernoulli distributions in each state.

Learning from History Learning from History The initial prob. of being in each state, transition between

states, and output distribution in each state

Using the Baum-Welch algorithm (expectation maximization) Using the Baum-Welch algorithm (expectation maximization)

Trust CalculationTrust Calculation Probability of success: p

Trust: E[p] is calculated using the Forward-Backward algorithm.

)|Pr(

)|,Pr(),|Pr(

ΩΩ==Ω==

H

HxOHxOp


Case StudyCase Study10

Uncertainty of the Beta and HMM ModelsUncertainty of the Beta and HMM Models

Case StudyCase Study10


Quantification of UncertaintyQuantification of Uncertainty

Confidence IntervalConfidence Interval

A well-known indicator of probabilistic uncertainty.

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A well-known indicator of probabilistic uncertainty.

There is an almost general method to calculate them (bootstrapping).

Is not bound to a specific uncertainty factor.

Definition:Definition:

Δτ = [τ1, τ2] is the δ confidence interval of τ if:

δτττ =≤≤ )Pr(

Example: Example: 00..95 95 confidence interval of [confidence interval of [00..44, , 00..66]]

The real value is in [0.4,0.6] with probability 0.95

δτττ =≤≤ )Pr( 21


Real Trustee Simulation ModelReal Trustee Simulation Model12

Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili

Labels: b/m: benevolent/malicious, w/f: working, faulty

27 Mar. 2012

Average Confidence Interval Length Average Confidence Interval Length

(Varying (Varying ss))13

(n = 300 observations)Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012

Average Confidence Interval Length Average Confidence Interval Length

(Varying (Varying nn))14

(Stability s = 0.4)Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012

Summary of the Case StudiesSummary of the Case Studies

Great Amount of Uncertainty in Both ModelsGreat Amount of Uncertainty in Both Models

Especially with small history sizes (even with n = 100)

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Especially with small history sizes (even with n = 100)

The Beta model is more certain with small ns

Improving CertaintyImproving Certainty

Beta: No way! Forgetting factor is a fixed setting.

HMM: Enriching history with more observationsHMM: Enriching history with more observations


A ProposalA Proposal16

UncertaintyUncertainty--Driven Risk ReductionDriven Risk Reduction

A ProposalA Proposal16


Risk and TrustRisk and Trust17

Decision Risk = Uncertainty x CriticalityDecision Risk = Uncertainty x Criticality

Criticality: fixed Criticality: fixed

Uncertainty: can be reduced

LowMediumHigh

MediumHighHighHigh

Cri

tica

lity

Uncertainty

Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili

MediumMediumHighMedium

LowLowLowLowCri

tica

lity

Decision RiskDecision Risk

27 Mar. 2012

UncertaintyUncertainty--Driven Risk ReductionDriven Risk Reduction

Example Example

Utility function =+

=xo

ouunits 50

)(

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Utility function

Utility and Its UncertaintyUtility and Its Uncertainty

Expected utility:

Uncertainty: (interval arith.)

A Random Simulation SampleA Random Simulation Sample

)().1()(. xuxuU ττ −+=)().1()(. xuxuU ττ ∆−+∆=∆

=−

=xo

ouunits 20

)(

]67.0,29.0[48.0 bb =∆=τ A Random Simulation SampleA Random Simulation Sample

Beta and HMM trust:

Utility and uncertainty:]60.0,43.0[52.0

]67.0,29.0[48.0hh

bb

=∆==∆=

ττ

]06.22,15.10[35.16

]09.27,04.0[45.13hh

bb

=∆=−=∆=

U

U

U

U

Future Work and Open ProblemsFuture Work and Open Problems19 Future Work and Open ProblemsFuture Work and Open Problems19


Other Sources of UncertaintyOther Sources of Uncertainty

Model Uncertainty (Our Study)Model Uncertainty (Our Study) Uncertainty caused by induction and abstraction

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Uncertainty caused by induction and abstraction

Can consider significance of hypothesis testing

Uncertainty in ObservationsUncertainty in Observations Monitoring Systems: random and systematic errors

Human Feedback: fuzziness and vagueness

Credibility of Information SourcesCredibility of Information Sources Path-length in trust inference Path-length in trust inference

Up-to-date information (time)

We Seek for an Integrated Model for All These We Seek for an Integrated Model for All These Uncertainty Types and SourcesUncertainty Types and Sources


ConclusionsConclusions

Uncertainty Is an Inherent Feature of TrustUncertainty Is an Inherent Feature of Trust

Uncertainty of trustee

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Uncertainty of trustee

Uncertainty of models

Uncertainty Has Severe Effect on Existing ModelsUncertainty Has Severe Effect on Existing Models

Beta and HMM

Uncertainty Can be Used in conjunction with Trust Uncertainty Can be Used in conjunction with Trust Uncertainty Can be Used in conjunction with Trust Uncertainty Can be Used in conjunction with Trust

InformationInformation

In decision-making and consideration of risk


Thanks!Thanks!22

My Homepage My Homepage

http://ce.sharif.edu/~dorrihttp://ce.sharif.edu/~dorri

Thanks!Thanks!22


ReferencesReferences

[ESN[ESN1010] E. ] E. ElSalamounyElSalamouny, V. , V. SassoneSassone, and M. Nielsen, , and M. Nielsen,

“HMM“HMM--based trust model,” Formal Aspects in Security based trust model,” Formal Aspects in Security

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“HMM“HMM--based trust model,” Formal Aspects in Security based trust model,” Formal Aspects in Security

and Trust, vol. and Trust, vol. 59835983, pp. , pp. 2121--3535, , 20102010..

[Gam[Gam9090] D. Gambetta, “Can we trust ] D. Gambetta, “Can we trust trusttrust,” in Trust: ,” in Trust:

Making and breaking cooperative relations, Oxford, Making and breaking cooperative relations, Oxford,

UK: Basil Blackwell, UK: Basil Blackwell, 19901990, pp. , pp. 213213––237237..

[JI[JI0202] A. ] A. JøsangJøsang and R. Ismail, “The Beta Reputation and R. Ismail, “The Beta Reputation [JI[JI0202] A. ] A. JøsangJøsang and R. Ismail, “The Beta Reputation and R. Ismail, “The Beta Reputation

System,” in Proceedings of the System,” in Proceedings of the 1515th Bled Conference th Bled Conference

on Electronic Commerce, Bled, Slovenia, on Electronic Commerce, Bled, Slovenia, 20022002..


Uncertainty in Probabilistic Trust Models

Engineering

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