Abstract: 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. 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 in the context of DGMs. We compare our algorithm with a standard data-independent approach over a diverse suite of benchmarks and demonstrate that our solution requires a privacy budget that is roughly $3\times$ smaller to obtain the same or higher utility.