This document presents two probabilistic trust models - the Beta model and the Hidden Markov Model (HMM) - and analyzes the uncertainty inherent in these models. Through case studies, it is shown that both models exhibit a great amount of uncertainty, especially with small histories. The uncertainty can be reduced in the HMM by enriching the history with more observations. The document proposes an uncertainty-driven approach to risk reduction by considering both the trust value and the uncertainty around it when making decisions. Future work directions include integrating different sources of uncertainty into a unified model.
1. In the Name of AllahIn the Name of Allah
Data and NetworkData and Network
Security Lab. (DNSL)Security Lab. (DNSL)
Sharif UniversitySharif University
of 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
2. Who Knows on the Net...?Who Knows on the Net...?
A notion of trust similar toA notion of trust similar to
real world trust isreal world trust is
2
real world trust isreal world trust is
needed in the virtualneeded in the virtual
world…world…
Coordinating AgentCoordinating Agent
Interactions withoutInteractions without
Strict ControlStrict Control
MechanismsMechanismsMechanismsMechanisms
Fig. by Peter Steiner (The New Yorker, 5 July 1993)
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
3. Uncertainty and TrustUncertainty and Trust
Uncertainty = Lack of InformationUncertainty = Lack of Information
Randomness, fuzziness, vagueness, ambiguity
3
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
4. OutlineOutline
BackgroundBackground
Probabilistic trust framework
4
Probabilistic trust framework
Case StudyCase Study
Uncertainty in two prob. trust models
A ProposalA Proposal
Uncertainty-driven risk reduction with trustUncertainty-driven risk reduction with trust
Future WorkFuture Work
Other forms of uncertainty
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
6. Trust ScenarioTrust Scenario
Direct Trust
6
Trustor Trustee
Direct Trust
Functional
Referential Functional
Functional
Indirect Trust (Inference)
Referential Functional
Recommenders
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
7. Probabilistic Trust FrameworkProbabilistic Trust Framework
Definition of Trust (Adopted from [GamDefinition of Trust (Adopted from [Gam9090]):]):
The subjective probability by which trustor expects that
7
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
tn
tetr
t
tetr
t
tetr
t OOxOp …==
][ ,, tetrtetr
pE=τTrust (Bayesian view)
From now on, a specificFrom now on, a specific trtr,, tete, and, and tt are implicitlyare implicitly
assumed.assumed.
][ ,, tetr
t
tetr
t pE=τ
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
8. 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
8
Hence,Hence, pp Follows the Beta DistributionFollows the Beta Distribution
r: success outcomes
s: failure outcomes
Trust 1
]E[
+
==
r
pτ
=−
=
==
xop
xop
oO
1
)Pr(
sr
pp
sr
sr
pf )1(
)1()1(
)2(
)( −
+Γ+Γ
++Γ
=
Trust
Change of Trustee BehaviorChange of Trustee Behavior
Forgetting facotr (λ)
2
]E[
++
==
sr
pτ
)(
)(
}{)1(
}{)1(
tnxnttn
tnxnttn
OIss
OIrr
+=
+=
−
−
λ
λ
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
9. The HMM Trust Model [ESNThe HMM Trust Model [ESN1010]]
Trustee Is Modeled with aTrustee Is Modeled with a 22--State Hidden Markov ModelState Hidden Markov Model
(HMM)(HMM) –– ΩΩ
2 (hidden) states (benevolent/malicious)
9
2 (hidden) states (benevolent/malicious)
2 possible outputs with independent Bernoulli distributions in
each state.
Learning from HistoryLearning 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(
Ω
Ω=
=Ω==
H
HxO
HxOp
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
10. 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
11. Quantification of UncertaintyQuantification of Uncertainty
Confidence IntervalConfidence Interval
A well-known indicator of probabilistic uncertainty.
11
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..9595 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
12. Real Trustee Simulation ModelReal Trustee Simulation Model
12
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
Labels: b/m: benevolent/malicious, w/f: working, faulty
27 Mar. 2012
13. Average Confidence Interval LengthAverage Confidence Interval Length
(Varying(Varying ss))13
(n = 300 observations)
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
14. Average Confidence Interval LengthAverage Confidence Interval Length
(Varying(Varying nn))14
(Stability s = 0.4)
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
15. 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)
15
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
17. Risk and TrustRisk and Trust
17
Decision Risk = Uncertainty x CriticalityDecision Risk = Uncertainty x Criticality
Criticality: fixedCriticality: fixed
Uncertainty: can be reduced
LowMediumHigh
MediumHighHighHigh
Criticality
Uncertainty
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
MediumMediumHighMedium
LowLowLowLow
Criticality
Decision RiskDecision Risk
27 Mar. 2012
18. UncertaintyUncertainty--Driven Risk ReductionDriven Risk Reduction
ExampleExample
Utility function
=+
=
xo
ou
units50
)(
18
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
ou
units20
)(
]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[48.0
hh
bb
=∆=
=∆=
τ
τ
]06.22,15.10[35.16
]09.27,04.0[45.13
hh
bb
=∆=
−=∆=
U
U
U
U
19. 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
20. Other Sources of UncertaintyOther Sources of Uncertainty
Model Uncertainty (Our Study)Model Uncertainty (Our Study)
Uncertainty caused by induction and abstraction
20
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 inferencePath-length in trust inference
Up-to-date information (time)
We Seek for an Integrated Model for All TheseWe 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
21. ConclusionsConclusions
Uncertainty Is an Inherent Feature of TrustUncertainty Is an Inherent Feature of Trust
Uncertainty of trustee
21
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 TrustUncertainty Can be Used in conjunction with TrustUncertainty Can be Used in conjunction with TrustUncertainty 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
23. ReferencesReferences
[ESN[ESN1010] E.] E. ElSalamounyElSalamouny, V., V. SassoneSassone, and M. Nielsen,, and M. Nielsen,
“HMM“HMM--based trust model,” Formal Aspects in Securitybased trust model,” Formal Aspects in Security
23
“HMM“HMM--based trust model,” Formal Aspects in Securitybased 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 Reputationand R. Ismail, “The Beta Reputation[JI[JI0202] A.] A. JøsangJøsang and R. Ismail, “The Beta Reputationand R. Ismail, “The Beta Reputation
System,” in Proceedings of theSystem,” in Proceedings of the 1515th Bled Conferenceth 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