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Finite mixture models are statistical models which appear in many problems instatistics and machine learning. In such models it is assumed that data aredrawn from random probability measures, called mixture components, which arethemselves drawn from a probability measure P over probability measures. Whenestimating mixture models, it is common to make assumptions on the mixturecomponents, such as parametric assumptions. In this paper, we make noassumption on the mixture components, and instead assume that observations fromthe mixture model are grouped, such that observations in the same group areknown to be drawn from the same component. We show that any mixture of mprobability measures can be uniquely identified provided there are 2m-1observations per group. Moreover we show that, for any m, there exists amixture of m probability measures that cannot be uniquely identified whengroups have 2m-2 observations. Our results hold for any sample space with morethan one element.

On The Identifiability of Mixture Models from Grouped Samples