uncertainty in probabilistic trust models
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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
2
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
BackgroundBackground5
Probabilistic Trust FrameworkProbabilistic Trust Framework
BackgroundBackground5
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
Case StudyCase Study10
Uncertainty of the Beta and HMM ModelsUncertainty of the Beta and HMM Models
Case StudyCase Study10
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
A ProposalA Proposal16
UncertaintyUncertainty--Driven Risk ReductionDriven Risk Reduction
A ProposalA Proposal16
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
Thanks!Thanks!22
My Homepage My Homepage
http://ce.sharif.edu/~dorrihttp://ce.sharif.edu/~dorri
Thanks!Thanks!22
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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
23
“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 Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
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