mlsanityData to 14 Oct 2026

Generalized Identifiability Bounds for Mixture Models with Grouped Samples

arXiv 2207.11164 ↗First posted 22 Jul 2022math.ST cs.LG stat.MLcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 23 of its 71 references that are in the map. First posted on arXiv 22 Jul 2022.

Builds on

23 of 71 references.

References · 23

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11 more
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Citing papers per year: 2023: 1; 2024: 0; 2025: 1.

2 papers.

  1. 2023Sample Complexity Using Infinite Multiview Modelscited by 3
  2. 2025PMODE: Theoretically Grounded and Modular Mixture Modelingcited by 1