TIDY: Publishing a Time Interval Dataset with Differential Privacy

Log data from mobile devices generally contain a series of events with temporal information including time intervals which consist of the start and finish times. However, the problem of releasing differentially private time interval datasets has not been tackled yet. A time interval dataset can be represented by a two dimensional (2D) histogram. Most of the methods to publish 2D histograms partition the data into rectangular spaces to reduce the aggregated noise error for range queries. However, the existing algorithms to publish 2D histograms suffer from the structural error when applied to time interval datasets. To reduce the aggregated noise errors and suppress the increase in the structural error, we propose the TIDY (publishing Time Intervals via Differential privacY) algorithm. We use the frequency vectors as a compact representation of the time interval dataset. After applying the Laplace mechanism to the frequency vectors, we improve the utility of the frequency vectors based on a maximum likelihood estimation. We also develop a new partitioning method adapted for the frequency vectors to balance the trade-off between the noise and structural errors. Our empirical study on real-life and synthetic datasets confirms that TIDY outperforms the existing algorithms for 2D histograms.