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Actually, All Learnable Distribution Classes Are Privately Learnable

Mohammad Afzali, Hassan Ashtiani, Alex Bie, Gautam Kamath, Peihan Liu, Argyris Mouzakis, Vikrant Singhal · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28878 · cited by 0 works (OpenAlex) · open-access PDF

Indonesian

Kami menunjukkan bahwa setiap kelas distribusi yang dapat dipelajari sampai dengan kesalahan target yang kecil secara arbitrase dalam jarak variasi total dengan sampel yang banyak juga dapat dipelajari di bawah ($\varepsilon, δ$)-privasi diferensial sampai dengan kesalahan target yang kecil secara arbitrase dengan sampel yang banyak. Ini membuktikan dugaan Ashtiani. pekerjaan sebelumnya oleh Bun, Kamath, Mouzakis, dan Singhal [arXiv:2402.00267] memberikan penolakan yang lemah dari dugaan ini, menunjukkan bahwa implikasi ini tidak benar ketika pembelajaran didefinisikan sehubungan dengan kesalahan target tetap. Sebaliknya, kami menunjukkan bahwa, di bawah definisi standar pembelajaran, dugaan ini benar.

Machine translation (Meta M2M100); the English original follows.

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 ($\varepsilon, δ$)-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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Topics: Mathematics, Conjecture, Learnability, Combinatorics, Discrete mathematics, Class (philosophy)

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