Oliver Mason

Nathan McJames, David Malone, Oliver Mason

The rankability of data is a recently proposed problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have recently been proposed, based on comparisons to a complete dominance graph via combinatorial and linear algebraic methods. In this paper, we review these measures and highlight some questions to which they give rise before going on to propose new methods to assess rankability, which are amenable to efficient estimation. Finally, we compare these measures by applying them to both synthetic and real-life sports data.

Aisling Mc Glinchey, Oliver Mason

We study two methods for differentially private analysis of bounded data and extend these to nonnegative queries. We first recall that for the Laplace mechanism, boundary inflated truncation (BIT) applied to nonnegative queries and truncation both lead to strictly positive bias. We then consider a generalization of BIT using translated ramp functions. We explicitly characterise the optimal function in this class for worst case bias. We show that applying any square-integrable post-processing function to a Laplace mechanism leads to a strictly positive maximal absolute bias. A corresponding result is also shown for a generalisation of truncation, which we refer to as restriction. We also briefly consider an alternative approach based on multiplicative mechanisms for positive data and show that, without additional restrictions, these mechanisms can lead to infinite bias.

Naoise Holohan, Douglas J. Leith, Oliver Mason

We examine a generalised Randomised Response (RR) technique in the context of differential privacy and examine the optimality of such mechanisms. Strict and relaxed differential privacy are considered for binary outputs. By examining the error of a statistical estimator, we present closed solutions for the optimal mechanism(s) in both cases. The optimal mechanism is also given for the specific case of the original RR technique as introduced by Warner in 1965.

Naoise Holohan, Doug Leith, Oliver Mason

We study mechanisms for differential privacy on finite datasets. By deriving \emph{sufficient sets} for differential privacy we obtain necessary and sufficient conditions for differential privacy, a tight lower bound on the maximal expected error of a discrete mechanism and a characterisation of the optimal mechanism which minimises the maximal expected error within the class of mechanisms considered.