  Joint distribution estimation of a dataset under differential privacy is a
fundamental problem for many privacy-focused applications, such as query
answering, machine learning tasks and synthetic data generation. In this work,
we examine the joint distribution estimation problem given two data points: 1)
differentially private answers of a workload computed over private data and 2)
a prior empirical distribution from a public dataset. Our goal is to find a new
distribution such that estimating the workload using this distribution is as
accurate as the differentially private answer, and the relative entropy, or KL
divergence, of this distribution is minimized with respect to the prior
distribution. We propose an approach based on iterative optimization for
solving this problem. An application of our solution won second place in the
NIST 2020 Differential Privacy Temporal Map Challenge, Sprint 2.
