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In the context of a finite admixture model whose components and weights areunknown, if the number of identifiable components is a function of the amountof data collected, we use techniques from stochastic convex geometry to findthe growth rate of its expected value. In addition, when the components areknown but the weights are not, we provide an application of the classicGlivenko-Cantelli's theorem that allows us to retrieve the Choquet measuresupported on the identifiable admixture components. In turn, this gives us theidentifiable admixture weights. Finally, we propose a novel algorithm thatestimates the model capturing the complexity of the data using only thestrictly necessary number of components.

Finite admixture models: a bridge with stochastic geometry and Choquet theory