Not All Learnable Distribution Classes are Privately Learnable

Mark Bun, Gautam Kamath, Argyris Mouzakis, Vikrant Singhal

Abstract: We give an example of a class of distributions that is learnable in total variation distance with a finite number of samples, but not learnable under $(\varepsilon, \delta)$-differential privacy. This refutes a conjecture of Ashtiani.