Differentially Private Heatmaps

TL;DR

This paper introduces a differentially private algorithm for generating heatmaps from user data, balancing privacy and accuracy, and demonstrates its effectiveness on real datasets with near-optimal error bounds.

Contribution

It presents a novel DP procedure for aggregating distributions into heatmaps with theoretical error bounds and practical advantages over existing methods.

Findings

The DP algorithm produces heatmaps with low Earth Mover's Distance error.

Theoretical bounds on error are near-optimal under sparsity assumptions.

Algorithm outperforms previous methods on real-world datasets.

Abstract

We consider the task of producing heatmaps from users' aggregated data while protecting their privacy. We give a differentially private (DP) algorithm for this task and demonstrate its advantages over previous algorithms on real-world datasets. Our core algorithmic primitive is a DP procedure that takes in a set of distributions and produces an output that is close in Earth Mover's Distance to the average of the inputs. We prove theoretical bounds on the error of our algorithm under a certain sparsity assumption and that these are near-optimal.