Information preservation in statistical privacy and bayesian estimation of unattributed histograms

Abstract

In statistical privacy, utility refers to two concepts: information preservation -how much statistical information is retained by a sanitizing algorithm, and usability -how (and with how much difficulty) does one extract this information to build statistical models, answer queries, etc. Some scenarios incentivize a separation between information preservation and usability, so that the data owner first chooses a sanitizing algorithm to maximize a measure of information preservation and, afterward, the data consumers process the sanitized output according to their needs [22,46].We analyze a variety of utility measures and show that the average (over possible outputs of the sanitizer) error of Bayesian decision makers forms the unique class of utility measures that satisfy three axioms related to information preservation. The axioms are agnostic to Bayesian concepts such as subjective probabilities and hence strengthen support for Bayesian views in privacy research. In particular, this result connects information preservation to aspects of usability -if the information preservation of a sanitizing algorithm should be measured as the average error of a Bayesian decision maker, shouldn't Bayesian decision theory be a good choice when it comes to using the sanitized outputs for various purposes? We put this idea to the test in the unattributed histogram problem where our decisiontheoretic post-processing algorithm empirically outperforms previously proposed approaches.

Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation

“…Intuitively, edge differential privacy ensures that an algorithm's output does not reveal the inclusion or removal of a particular edge in the graph, while node differential privacy hides the inclusion or removal of a node together with all its adjacent edges. Edge privacy is weaker (hence easier to achieve) and has been studied more extensively [47,50,34,45,43,35,28,29,33,40,32,27,7,45,35,43,32,55].…”

Differentially private hierarchical count-of-counts histograms

“…The work most closely related to our problem are unattributed histograms [19,8] which are often used to study degree sequences in social networks [24,21]. Unattributed histograms are the duals of count-of-counts queries (they count people rather than groups) and can be used to answer queries such as "what is the size of the k th largest group?"…”

“…Hg=SELECT COUNT(*) AS size FROM R GROUPBY groupid ORDERBY size. One can convert unattributed histograms into count-of-counts histograms and vice-versa, so differentially private unattributed histograms [19,24] could be used to generate differentially private count-of-counts histograms (and vice versa, see Section 4.2).…”

Private Release of Graph Statistics using Ladder Functions

“…This paper and subsequent related approaches [18,22] provide effective solutions to releasing the degree sequence of a sensitive graph, and use some sophisticated postprocessing techniques to reduce noise. Proserpio et al [31] and Sala et al [33] further extend the problem to higher-order joint degree sequences, which model more detailed information within the sensitive graph.…”