Abstract
The scientific and economic value of data continues to grow alongside technology advances. New hardware and software developments enable, but often require, larger and more complex datasets to function effectively. As the importance of input data to these systems becomes increasingly recognized, so too does the loss of privacy for data providers. In this context, data privacy emerges as a critical issue for fields such as statistics and machine learning, as well as for scientific and industrial endeavours that rely on sensitive data. We propose a framework for measuring privacy from a Bayesian decision-theoretic perspective. This framework enables the creation of new, purpose-driven privacy principles that are rigorously justified, while also allowing for the assessment of existing privacy definitions through decision theory. We pay particular attention to the privacy of deterministic algorithms, which are overlooked by current privacy standards, and to the privacy of N Monte Carlo samples drawn from an invariant distribution as N goes to infinity. We show that Probabilistic Differential Privacy is a special case of our framework and provide some new interpretations for Differential Privacy as a result.
