  Directed graphical models (DGMs) are a class of probabilistic models that are
widely used for predictive analysis in sensitive domains, such as medical
diagnostics. In this paper we present an algorithm for differentially private
learning of the parameters of a DGM with a publicly known graph structure over
fully observed data. Our solution optimizes for the utility of inference
queries over the DGM and \textit{adds noise that is customized to the
properties of the private input dataset and the graph structure of the DGM}. To
the best of our knowledge, this is the first explicit data-dependent privacy
budget allocation algorithm for DGMs. We compare our algorithm with a standard
data-independent approach over a diverse suite of DGM benchmarks and
demonstrate that our solution requires a privacy budget that is $3\times$
smaller to obtain the same or higher utility.
