Not All Learnable Distribution Classes are Privately Learnable
Data Structures and Algorithms
2026-05-20 v4 Cryptography and Security
Machine Learning
Abstract
We give an example of a class of distributions that is learnable up to constant error in total variation distance with a finite number of samples, but not learnable under -differential privacy with the same target error. This weakly refutes a conjecture of Ashtiani.
Cite
@article{arxiv.2402.00267,
title = {Not All Learnable Distribution Classes are Privately Learnable},
author = {Mark Bun and Gautam Kamath and Argyris Mouzakis and Vikrant Singhal},
journal= {arXiv preprint arXiv:2402.00267},
year = {2026}
}
Comments
Appeared in ALT 2024. Fixed a bug and improved exposition. Same version as the one in AM's PhD thesis