An analysis of the exponential decay principle in probabilistic trust models

Abstract

a b s t r a c tResearch in models for experience-based trust management has either ignored the problem of modelling and reasoning about dynamically changing principal behaviour, or provided ad hoc solutions to it. Probability theory provides a foundation for addressing this and many other issues in a rigorous and mathematically sound manner. Using Hidden Markov Models to represent principal behaviours, we focus on computational trust frameworks based on the 'beta' probability distribution and the principle of exponential decay, and derive a precise analytical formula for the estimation error they induce. This allows potential adopters of beta-based computational trust frameworks and algorithms to better understand the implications of their choice.

Node Trust Assessment and Prediction in Mobile Ad Hoc Networks

“…(1) Choose the last four data nearest to the prediction time as initial states, and obtain the transition probability of each data according to the transition probability matrix P (1) , P (2) , P (3) and P (4) . Then we can calculate the sum of transition probability for each state shown in the following Table 6: As shown in the above Table 6, the biggest number in the sum of transition probability is 1.82.…”

An HMM-Based Reputation Model

“…It is also apparent from Figure 3, that incorporating a decay factor in the Beta model (viz., 0.9 in the example) reduces the expected estimation error. Further details about the effect of decay can be found in [7].…”

“…It aims at capturing the recent behaviour of the trustee by letting older observations 'decay', so as to give higher weight to recent interactions over older ones. However, we showed in [7] that the decay principle is only useful when the trustee's behaviour is highly stable, i.e, when the probability distribution over the observables is unlikely to change.…”

Secure Trust-based Cooperative Communications in Wireless Multi-Hop Networks

“…The node whose trust value achieves the highest will be set as the central node (Chang, Kuo, 2009). ElSalamouny et al adopts a sort of potential Markov Chain to indicate the key behaviour of the node, and makes use of the beta probability distribution and exponential decay to evaluate the trust error (ElSalamouny, Krukow, et al, 2009). However, neither of these two reputation models involves node attacks.…”