Differentially Private Learning of Undirected Graphical Models Using Collective Graphical Models

We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the noisy sufficient statistics “as is” outperforms general-purpose differentially private learning algorithms. However, it has three limitations: it ignores knowledge about the data generating process, rests on uncertain theoretical foundations, and exhibits certain pathologies. We develop a more principled approach that applies the formalism of collective graphical models to perform inference over the true sufficient statistics within an expectationmaximization framework. We show that this learns better models than competing approaches on both synthetic data and on real human mobility data used as a case study.