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We investigate the problem of learning discrete, undirected graphical modelsin a differentially private way. We show that the approach of releasing noisysufficient statistics using the Laplace mechanism achieves a good trade-offbetween privacy, utility, and practicality. A naive learning algorithm thatuses the noisy sufficient statistics "as is" outperforms general-purposedifferentially private learning algorithms. However, it has three limitations:it ignores knowledge about the data generating process, rests on uncertaintheoretical foundations, and exhibits certain pathologies. We develop a moreprincipled approach that applies the formalism of collective graphical modelsto perform inference over the true sufficient statistics within anexpectation-maximization framework. We show that this learns better models thancompeting approaches on both synthetic data and on real human mobility dataused as a case study.

Differentially Private Learning of Undirected Graphical Models using Collective Graphical Models