  Mixed membership models are an extension of finite mixture models, where each
observation can partially belong to more than one mixture component. A
probabilistic framework for mixed membership models of high-dimensional
continuous data is proposed with a focus on scalability and interpretability.
The novel probabilistic representation of mixed membership is based on convex
combinations of dependent multivariate Gaussian random vectors. In this
setting, scalability is ensured through approximations of a tensor covariance
structure through multivariate eigen-approximations with adaptive
regularization imposed through shrinkage priors. Conditional weak posterior
consistency is established on an unconstrained model, allowing for a simple
posterior sampling scheme while keeping many of the desired theoretical
properties of our model. The model is motivated by two biomedical case studies:
a case study on functional brain imaging of children with autism spectrum
disorder (ASD) and a case study on gene expression data from breast cancer
tissue. These applications highlight how the typical assumption made in cluster
analysis, that each observation comes from one homogeneous subgroup, may often
be restrictive in several applications, leading to unnatural interpretations of
data features.
