2 research outputs found
Generalized Identifiability Bounds for Mixture Models with Grouped Samples
Recent work has shown that finite mixture models with components are
identifiable, while making no assumptions on the mixture components, so long as
one has access to groups of samples of size which are known to come from
the same mixture component. In this work we generalize that result and show
that, if every subset of mixture components of a mixture model are linearly
independent, then that mixture model is identifiable with only
samples per group. We further show that this value cannot be improved. We prove
an analogous result for a stronger form of identifiability known as
"determinedness" along with a corresponding lower bound. This independence
assumption almost surely holds if mixture components are chosen randomly from a
-dimensional space. We describe some implications of our results for
multinomial mixture models and topic modeling