
On The Identifiability of Mixture Models from Grouped Samples
Finite mixture models are statistical models which appear in many proble...
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On the Identifiability of Finite Mixtures of Finite Product Measures
The problem of identifiability of finite mixtures of finite product meas...
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Penalized Component Hub Models
Social network analysis presupposes that observed social behavior is inf...
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Estimating the Number of Components in Finite Mixture Models via the GroupSortFuse Procedure
Estimation of the number of components (or order) of a finite mixture mo...
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Network Inference from TemporalDependent Grouped Observations
In social network analysis, the observed data is usually some social beh...
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On the Bias of the Score Function of Finite Mixture Models
We characterize the unbiasedness of the score function, viewed as an inf...
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On Coarse Graining of Information and Its Application to Pattern Recognition
We propose a method based on finite mixture models for classifying a set...
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Identifiability and consistency of network inference using the hub model and variants: a restricted class of Bernoulli mixture models
Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko (2019) propose a modelbased approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is brought together by a member of the group called the hub. The hub model belongs to the family of Bernoulli mixture models. Identifiability of parameters is a notoriously difficult problem for Bernoulli mixture models. This paper proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this paper generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model – the Bernoulli product. Identifiability and consistency are also proved for the new model. Numerical studies are provided to demonstrate the theoretical results.
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