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arXiv Statistics ML By Yaiza Bermudez, Samir M. Perlaza, I\~naki Esnaola

Equivalence Between Nested Gibbs Measures and Log-Linear Combinations of Gibbs Measures

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The paper investigates three operations on Gibbs probability measures: renormalization, normalized log-linear combination, and nesting (changing the reference measure). It shows that the measures produced by the second and third operations solve related optimization problems and that, for specific parameters, nesting one Gibbs measure into another is equivalent to log-linearly combining them. This equivalence has practical implications, such as enabling a one-shot federated learning system where clients’ locally trained Gibbs algorithms can be combined on a server to match the performance of a centrally trained Gibbs algorithm.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Statistics ML.

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