Calculating Probabilistic Anonymity From Sampled Data
This paper addresses the problem of calculating the anonymity of a system statistically from a number of trial runs. The authors show that measures of anonymity based on capacity can be estimated, by showing that the Blahut-Arimoto algorithm converges for sampled data. They obtain bounds on the error of the estimated value by calculating the distribution of mutual information when one distribution is known and one unknown. This leads to finding the variance of the estimation of anonymity in terms of the numbers of samples, inputs and possible observations, which in turn tells them what kinds of systems can and cannot be accurately analyzed using a statistical approach.