  Aggregating a dataset, then injecting some noise, is a simple and common way
to release differentially private data.However, aggregated data -- even without
noise -- is not an appropriate input for machine learning classifiers.In this
work, we show how a new model, similar to a logistic regression, may be learned
from aggregated data only by approximating the unobserved feature distribution
with a maximum entropy hypothesis. The resulting model is a Markov Random Field
(MRF), and we detail how to apply, modify and scale a MRF training algorithm to
our setting. Finally we present empirical evidence on several public datasets
that the model learned this way can achieve performances comparable to those of
a logistic model trained with the full unaggregated data.
