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On the Identifiability of Finite Mixtures of Finite Product Measures. (arXiv:1807.05444v1 [math.ST])
来源于:arXiv
The problem of identifiability of finite mixtures of finite product measures
is studied. A mixture model with $K$ mixture components and $L$ observed
variables is considered, where each variable takes its value in a finite set
with cardinality $M$.The variables are independent in each mixture component.
The identifiability of a mixture model means the possibility of attaining the
mixture components parameters by observing its mixture distribution. In this
paper, we investigate fundamental relations between the identifiability of
mixture models and the separability of their observed variables by introducing
two types of separability: strongly and weakly separable variables. Roughly
speaking, a variable is said to be separable, if and only if it has some
differences among its probability distributions in different mixture
components. We prove that mixture models are identifiable if the number of
strongly separable variables is greater than or equal to $2K-1$, independent
form $M$. This f 查看全文>>