# Learning from aggregated data with a maximum entropy model

arXiv: https://arxiv.org/abs/2210.02450 · HTML: https://mlsanity.com/paper/2210.02450/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 6 of 6)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Graphical-model based estimation and inference for differential privacy](https://mlsanity.com/paper/1901.09136/) (2019)
- [Learning from Aggregate Observations](https://mlsanity.com/paper/2004.06316/) (2020)
- [Differentially Private Learning of Undirected Graphical Models using Collective Graphical Models](https://mlsanity.com/paper/1706.04646/) (2017)
- [Lessons from the AdKDD'21 Privacy-Preserving ML Challenge](https://mlsanity.com/paper/2201.13123/) (2022)
- [Logistic regression models for aggregated data](https://mlsanity.com/paper/1912.03805/) (2019)

## Abstract (arXiv)

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.