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PreprintCC BY-SA 4.0arXiv

Actually, All Learnable Distribution Classes Are Privately Learnable

  • Mohammad Afzali
  • Hassan Ashtiani
  • Alex Bie
  • Gautam Kamath
  • Peihan Liu
  • Argyris Mouzakis
  • Vikrant Singhal
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Abstract

We show that every class of distributions that is learnable up to arbitrarily small target error in total variation distance with finitely many samples is also learnable under (ε, δ)-differential privacy up to arbitrarily small target error with finitely many samples. This proves a conjecture of Ashtiani. Previous work by Bun, Kamath, Mouzakis, and Singhal [arXiv:2402.00267] gave a weak refutation of this conjecture, showing that this implication is not true when learnability is defined with respect to a fixed target error. In contrast, we show that, under the standard definition of learnability, the conjecture is true.

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Cite

BibTeXRIS
BibTeX
@misc{afzali2026actually,
  title = {{Actually, All Learnable Distribution Classes Are Privately Learnable}},
  author = {Mohammad Afzali and Hassan Ashtiani and Alex Bie and Gautam Kamath and Peihan Liu and Argyris Mouzakis and Vikrant Singhal},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28878},
  eprint = {2610.28878},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28878},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Actually, All Learnable Distribution Classes Are Privately Learnable
AU  - Mohammad Afzali
AU  - Hassan Ashtiani
AU  - Alex Bie
AU  - Gautam Kamath
AU  - Peihan Liu
AU  - Argyris Mouzakis
AU  - Vikrant Singhal
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28878
UR  - https://arxiv.org/abs/2610.28878
AB  - We show that every class of distributions that is learnable up to arbitrarily small target error in total variation distance with finitely many samples is also learnable under (ε, δ)-differential privacy up to arbitrarily small target error with finitely many samples. This proves a conjecture of Ashtiani. Previous work by Bun, Kamath, Mouzakis, and Singhal [arXiv:2402.00267] gave a weak refutation of this conjecture, showing that this implication is not true when learnability is defined with respect to a fixed target error. In contrast, we show that, under the standard definition of learnability, the conjecture is true.
ER  -