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Data-Dependent Differentially Private Parameter Learning for Directed Graphical Models

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.