  Differentially private algorithms for answering sets of predicate counting
queries on a sensitive database have many applications. Organizations that
collect individual-level data, such as statistical agencies and medical
institutions, use them to safely release summary tabulations. However, existing
techniques are accurate only on a narrow class of query workloads, or are
extremely slow, especially when analyzing more than one or two dimensions of
the data. In this work we propose HDMM, a new differentially private algorithm
for answering a workload of predicate counting queries, that is especially
effective for higher-dimensional datasets. HDMM represents query workloads
using an implicit matrix representation and exploits this compact
representation to efficiently search (a subset of) the space of differentially
private algorithms for one that answers the input query workload with high
accuracy. We empirically show that HDMM can efficiently answer queries with
lower error than state-of-the-art techniques on a variety of low and high
dimensional datasets.
