In the Name of Allah
Sharif University
of Technology
Data and Network
Security Lab. (DNSL)
Uncertainty in Probabilistic Trust Models
Sadegh Dorri Nogoorani, Rasool Jalili
Sharif University of Technology, Tehran, I.R. IRAN
http://ce.sharif.edu/~dorri
The 26th IEEE Int. Conf. Advanced Information Networking and Applications (AINA 2012)
Who Knows on the Net...?
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A notion of trust similar to
real world trust is
needed in the virtual
world…
Coordinating Agent
Interactions without
Strict Control
Mechanisms
Fig. by Peter Steiner (The New Yorker, 5 July 1993)
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Uncertainty and Trust
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Uncertainty = Lack of Information
Randomness, fuzziness, vagueness, ambiguity
Modeling 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 Trust
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
Outline
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Background
Probabilistic trust framework
Case Study
Uncertainty in two prob. trust models
A Proposal
Uncertainty-driven risk reduction with trust
Future Work
Other forms of uncertainty
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
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Background
Probabilistic Trust Framework
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Trust Scenario
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Direct Trust
Functional
Trustor
Indirect Trust (Inference)
Trustee
Functional
Functional
Referential
Recommenders
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Probabilistic Trust Framework
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Definition of Trust (Adopted from [Gam90
[Gam90]):
]):
The subjective probability by which trustor expects that
trustee performs a given action, on which its welfare
depends.
Trust: The (Expected) Probability of Positive Outcome
Action outcome:
R = { x, x }
Probability of success pttr ,te = Pr(Ottr ,te = x | Ottr1 ,te ,… , Otntr ,te )
Trust (Bayesian view) τ ttr ,te = E[ pttr ,te ]
From now on, a specific tr
tr,, te
te,, and t are implicitly
assumed.
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
The Beta Trust Model [JI02
[JI02]]
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Outcomes Assumed to be Bernoulli Trials (i.i.d
(i.i.d.)
.)
o=x
 p
Pr(O = o) = 
1 − p o = x
Hence, p Follows the Beta Distribution
r: success outcomes
s: failure outcomes
Trust
f ( p) =
Γ(r + s + 2)
p r (1 − p ) s
Γ(r + 1)Γ( s + 1)
τ = E[ p] =
Change of Trustee Behavior
Forgetting facotr (λ)
r +1
r+s+2
rtn = rt ( n −1) λ + I{ x} (Otn )
stn = st ( n −1) λ + I{ x } (Otn )
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
The HMM Trust Model [ESN10
[ESN10]]
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Trustee Is Modeled with a 2-State Hidden Markov Model
(HMM) – Ω
2 (hidden) states (benevolent/malicious)
2 possible outputs with independent Bernoulli distributions in
each state.
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)
Pr(O = x, H | Ω)
p = Pr(O = x | H , Ω) =
Pr( H | Ω)
Probability of success: p
Trust Calculation
Trust: E[p] is calculated using the Forward-Backward algorithm.
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
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Case Study
Uncertainty of the Beta and HMM Models
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Quantification of Uncertainty
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Confidence Interval
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:
Δτ = [τ1, τ2] is the δ confidence interval of τ if:
Pr(τ 1 ≤ τ ≤ τ 2 ) = δ
Example: 0.95 confidence interval of [0
[0.4, 0.6]
The real value is in [0.4,0.6] with probability 0.95
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Real Trustee Simulation Model
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Labels: b/m: benevolent/malicious, w/f: working, faulty
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Average Confidence Interval Length
(Varying s)
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(n = 300 observations)
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Average Confidence Interval Length
(Varying n)
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(Stability s = 0.4)
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Summary of the Case Studies
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Great Amount of Uncertainty in Both Models
Especially with small history sizes (even with n = 100)
The Beta model is more certain with small ns
Improving Certainty
Beta: No way! Forgetting factor is a fixed setting.
HMM: Enriching history with more observations
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
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A Proposal
Uncertainty--Driven Risk Reduction
Uncertainty
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Risk and Trust
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Decision Risk = Uncertainty x Criticality
Criticality: fixed
Uncertainty: can be reduced
Criticality
Uncertainty
High
Medium
Low
High
High
High
Medium
Medium
High
Medium
Medium
Low
Low
Low
Low
Decision Risk
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Uncertainty--Driven Risk Reduction
Uncertainty
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Example
Utility function
+ 50 units o = x
u (o) = 
− 20 units o = x
Utility and Its Uncertainty
U = τ .u ( x) + (1 − τ ).u ( x )
Expected utility:
Uncertainty: (interval arith.) ∆U = ∆τ .u ( x) + (1 − ∆τ ).u ( x )
A Random Simulation Sample
Beta and HMM trust:
Utility and uncertainty:
τ b = 0.48 ∆b = [0.29,0.67]
τ h = 0.52 ∆h = [0.43,0.60]
U b = 13.45 ∆bU = [−0.04,27.09]
U h = 16.35
∆hU = [10.15,22.06]
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Future Work and Open Problems
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Other Sources of Uncertainty
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Model Uncertainty (Our Study)
Uncertainty caused by induction and abstraction
Can consider significance of hypothesis testing
Uncertainty in Observations
Monitoring Systems: random and systematic errors
Human Feedback: fuzziness and vagueness
Credibility of Information Sources
Path-length in trust inference
Up-to-date information (time)
We Seek for an Integrated Model for All These
Uncertainty Types and Sources
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
Conclusions
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Uncertainty Is an Inherent Feature of Trust
Uncertainty of trustee
Uncertainty of models
Uncertainty Has Severe Effect on Existing Models
Beta and HMM
Uncertainty Can be Used in conjunction with Trust
Information
In decision-making and consideration of risk
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
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Thanks!
My Homepage
http://ce.sharif.edu/~dorri
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012
References
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[ESN10]] E. ElSalamouny
[ESN10
ElSalamouny,, V. Sassone
Sassone,, and M. Nielsen,
“HMM--based trust model,” Formal Aspects in Security
“HMM
and Trust, vol. 5983
5983,, pp. 21
21--35
35,, 2010.
2010.
[Gam90]] D. Gambetta, “Can we trust trust
[Gam90
trust,”
,” in Trust:
Making and breaking cooperative relations, Oxford,
UK: Basil Blackwell, 1990,
1990, pp. 213
213––237.
237.
[JI02]] A. Jøsang and R. Ismail, “The Beta Reputation
[JI02
System,” in Proceedings of the 15
15th
th Bled Conference
on Electronic Commerce, Bled, Slovenia, 2002
2002..
Uncertainty in Trust Models, Sadegh Dorri N., Rasool Jalili
27 Mar. 2012