On the Theory and Practice of Privacy-Preserving Bayesian Data Analysis. (arXiv:1603.07294v1 [cs.LG])

Bayesian inference has great promise for the privacy-preserving analysis of sensitive data, as posterior sampling automatically preserves differential privacy, an algorithmic notion of data privacy, under certain conditions (Wang et al., 2015). While Wang et al. (2015)'s one posterior sample (OPS) approach elegantly provides privacy "for free," it is data inefficient in the sense of asymptotic relative efficiency (ARE). We show that a simple alternative based on the Laplace mechanism, the workhorse technique of differential privacy, is as asymptotically efficient as non-private posterior inference, under general assumptions. The Laplace mechanism has additional practical advantages including efficient use of the privacy budget for MCMC. We demonstrate the practicality of our approach on a time-series analysis of sensitive military records from the Afghanistan and Iraq wars disclosed by the Wikileaks organization.

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