Learning from aggregated data with a maximum entropy model

Alexandre Gilotte (1) , Ahmed Ben Yamed (1) , David Rohde (1)

1 Criteo AI Lab

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.

Domaines: Intelligence artificielle [cs.AI]

Alexandre Gilotte, Ahmed Ben Yamed, David Rohde. Learning from aggregated data with a maximum entropy model. 2022. ⟨hal-03770740v2⟩