革新知能統合研究センター

Speaker: Koichi Tojo

Title: Invariant exponential families on homogeneous spaces
Abstract: Exponential families form a good class of families of
distributions.
Although, by definition, there are too many exponential families,
only a small part of them such as normal distributions and
gamma distributions are widely used. To understand these “good”
families systematically, a method to construct exponential families
on homogeneous spaces by representation theory was introduced in [TY18].
Families on a homogeneous space $G/H$ obtained by this method are
invariant under the action of the transformation group $G$.
Then the following natural question arises.
Question: Can $G$-invariant exponential families on $G/H$ be obtained by
this method?
In this talk, we give a quick review of this method and an affirmative
answer to the question above under a reasonable assumption.

[TY18] K. Tojo, T. Yoshino, A method to construct exponential families
by representation theory, arXiv:1811.01394

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