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Uncertainty in Probabilistic Trust Models

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Uncertainty in Probabilistic Trust Models

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PAPER: https://www.researchgate.net/publication/237075236_Uncertainty_in_Probabilistic_Trust_Models

Computational models of trust try to transfer the concept of trust from the real to the virtual world. While such models have been widely investigated in the past decade, the uncertainty involved in trust computation has been overlooked in the literature. In this paper, uncertainty of probabilistic trust models is quantified using confidence intervals and its factors are determined through simulation. The results confirm the importance and highlight the amount of uncertainty in the Beta and HMM (Hidden Markov Model) trust models. In addition, an uncertainty-driven method is proposed which reduces the risk involved in the trust-based utility maximization according to uncertainty.

PAPER: https://www.researchgate.net/publication/237075236_Uncertainty_in_Probabilistic_Trust_Models

Computational models of trust try to transfer the concept of trust from the real to the virtual world. While such models have been widely investigated in the past decade, the uncertainty involved in trust computation has been overlooked in the literature. In this paper, uncertainty of probabilistic trust models is quantified using confidence intervals and its factors are determined through simulation. The results confirm the importance and highlight the amount of uncertainty in the Beta and HMM (Hidden Markov Model) trust models. In addition, an uncertainty-driven method is proposed which reduces the risk involved in the trust-based utility maximization according to uncertainty.

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Uncertainty in Probabilistic Trust Models

  1. 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. 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. 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. 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
  5. 5. BackgroundBackground5 Probabilistic Trust FrameworkProbabilistic Trust Framework BackgroundBackground5 Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
  6. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
  16. 16. A ProposalA Proposal16 UncertaintyUncertainty--Driven Risk ReductionDriven Risk Reduction A ProposalA Proposal16 Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili 27 Mar. 2012
  17. 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. 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. 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. 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. 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
  22. 22. Thanks!Thanks!22 My HomepageMy 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
  23. 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

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