Randomized response is attractive for privacy preserving data collection
because the provided privacy can be quantified by means such as differential
privacy. However, recovering and analyzing statistics involving multiple
dependent randomized binary attributes can be difficult, posing a significant
barrier to use. In this work, we address this problem by identifying and
analyzing a family of response randomizers that change each binary attribute
independently with the same probability. Modes of Google's Rappor randomizer as
well as applications of two well-known classical randomized response methods,
Warner's original method and Simmons' unrelated question method, belong to this
family. We show that randomizers in this family transform multinomial
distribution parameters by an iterated Kronecker product of an invertible and
bisymmetric 2×2 matrix. This allows us to present a simple and
efficient algorithm for obtaining unbiased maximum likelihood parameter
estimates for k-way marginals from randomized responses and provide
theoretical bounds on the statistical efficiency achieved. We also describe the
efficiency - differential privacy tradeoff. Importantly, both randomization of
responses and the estimation algorithm are simple to implement, an aspect
critical to technologies for privacy protection and security.Comment: Accepted at Information Security - 21th International Conference, ISC
2018. Adapted to meet article length requirements. Fixed typo. Results
unchange