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Abstract:
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Partial membership models, or mixed membership models, are a flexible unsupervised learning method that allows observations to belong to multiple clusters at the same time. In this paper, we propose a Bayesian partial membership model for functional data. By using the multivariate Karhunen-Loève theorem, we are able to derive a scalable representation of Gaussian Processes that maintain data-driven learning of the covariance structure. Within this framework we establish conditional posterior consistency, given a known feature allocation matrix. Compared to previous work on partial membership models, our proposal allows for increased modeling flexibility, with the benefit of direct interpretation of the mean and covariance structure. Our work is 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.
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