UCLA

Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this dissertation, we propose a Bayesian mixed membership model for multivariate Gaussian data in Chapter 2 and functional data in Chapter 3. Compared to previous work on mixed membership models, our proposal allows for increased modeling flexibility, with the benefit of a directly interpretable mean and covariance structure. Our 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 probabilities. In Chapter 4, we extend the functional mixed membership model proposed in Chapter 3 to include covariate dependence. Using age as our covariate, we revisit the ASD study to illustrate the effect age has on alpha oscillations of developing children. The dissertation concludes with a discussion on possible extensions of the mixed membership framework in Chapter 5.