A1311
Title: Differentially private multivariate medians
Authors: Kelly Ramsay - York University (Canada) [presenting]
Shojaeddin Chenouri - University of Waterloo (Canada)
Dylan Spicker - University of New Brunswick (Saint John) (Canada)
Aukosh Jagannath - University of Waterloo (Canada)
Abstract: Data depth functions provide the standard framework for estimating a multivariate median. Currently, private versions are needed to allow for privacy-preserving, robust inference. Differentially private versions of various depth-based medians are explored, which are based on exponential mechanisms. In particular, the focus is on the theoretical properties, developing a general, tight finite sample deviations bound which can be applied to many depth-based medians at once, provided that the depths satisfy a simple condition. A method for relaxing this condition is also presented.
