Marcus Häggbom: Maximum-entropy distributions and Boltzmann equivalence

The ubiquity of the Gibbs distribution in statistics, in statistical physics also called the canonical ensemble, can be understood from many points of view. From an information-theoretic perspective, it is the maximum-entropy distribution subject to a moments constraint, and is therefore the model choice being maximally non-committed to missing information. Other constraints give rise to other maximum-entropy distributions, one being the microcanonical. This instead relies on a concentration assumption, where it is assumed that the energy is supported in a band. In this talk, I will discuss how these two distributions are used in generative machine learning, and, via theory of large deviations, present an equivalence between them in the case where the energy is defined in terms of a shift-invariant, finite range potential.