Mixed Membership Models with Applications to Neuroimaging

Music City Center 

Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this talk, we propose a Bayesian mixed membership model for functional data. Using the multivariate Karhunen-Loève theorem, we derived a scalable representation of Gaussian processes that maintains data-driven learning of the covariance structure. The work is primarily motivated by studies in functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD). In this context, our work formalizes the clinical notion of "spectrum" in terms of feature membership proportions. In addition, we discuss an extension of our framework to allow for covariate-dependent modeling structures. Within this framework, we established a set of sufficient conditions for ensuring the identifiability of the mean, covariance, and allocation structure up to a permutation of the labels. Using this covariate-dependent framework, we were able to gain novel insight into the developmental changes of neural activity as children age. Specifically, we found that typically developing children had a more prominent shift in peak alpha frequency, which has been shown to be a biomarker of neural development.

Mixed Membership Models

Functional Data Analysis

Clustering

Neuroimaging