  Differential Privacy (DP) formalizes privacy in mathematical terms and
provides a robust concept for privacy protection. DIfferentially Private Data
Synthesis (DIPS) techniques produce and release synthetic individual-level data
in the DP framework. One key challenge to developing DIPS methods is
preservation of the statistical utility of synthetic data, especially in
high-dimensional settings. We propose a new DIPS approach, STatistical Election
to Partition Sequentially (STEPS) that partitions data by attributes according
to their importance ranks according to either a practical or statistical
importance measure. STEPS aims to achieve better original information
preservation for the attributes with higher importance ranks and produce thus
more useful synthetic data overall. We present an algorithm to implement the
STEPS procedure and employ the privacy budget composability to ensure the
overall privacy cost is controlled at the pre-specified value. We apply the
STEPS procedure to both simulated data and the 2000-2012 Current Population
Survey youth voter data. The results suggest STEPS can better preserve the
population-level information and the original information for some analyses
compared to PrivBayes, a modified Uniform histogram approach, and the flat
Laplace sanitizer.
