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- W4288043152 abstract "Recent work has shown that finite mixture models with $m$ components are identifiable, while making no assumptions on the mixture components, so long as one has access to groups of samples of size $2m-1$ which are known to come from the same mixture component. In this work we generalize that result and show that, if every subset of $k$ mixture components of a mixture model are linearly independent, then that mixture model is identifiable with only $(2m-1)/(k-1)$ 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 $k$-dimensional space. We describe some implications of our results for multinomial mixture models and topic modeling." @default.
- W4288043152 created "2022-07-27" @default.
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- W4288043152 date "2022-07-22" @default.
- W4288043152 modified "2023-09-29" @default.
- W4288043152 title "Generalized Identifiability Bounds for Mixture Models with Grouped Samples" @default.
- W4288043152 doi "https://doi.org/10.48550/arxiv.2207.11164" @default.
- W4288043152 hasPublicationYear "2022" @default.
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