Covariate Adjusted Functional Mixed Membership Models

TL;DR

This paper introduces a covariate-dependent extension of functional mixed membership models, enabling analysis of heterogeneity in EEG alpha oscillations in children with autism spectrum disorder, accounting for age-related changes.

Contribution

It develops a scalable, covariate-adjusted functional mixed membership model using multivariate Karhunen-Loève decomposition, with conditions for identifiability and applications to EEG data.

Findings

Revealed developmental trajectories of alpha oscillations in children with ASD.

Differentiated heterogeneity patterns between ASD and typically developing children.

Provided a new framework for covariate-adjusted functional data analysis.

Abstract

Mixed membership models are a flexible class of probabilistic data representations used for unsupervised and semi-supervised learning, allowing each observation to partially belong to multiple clusters or features. In this manuscript, we extend the framework of functional mixed membership models to allow for covariate-dependent adjustments. The proposed model utilizes a multivariate Karhunen-Lo\`eve decomposition, which allows for a scalable and flexible model. Within this framework, we establish a set of sufficient conditions ensuring the identifiability of the mean, covariance, and allocation structure up to a permutation of the labels. This manuscript is primarily motivated by studies on functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD). Specifically, we are interested in characterizing the heterogeneity of alpha oscillations for typically developing (TD) children and children with ASD. Since alpha oscillations are known to change as children develop, we aim to characterize the heterogeneity of alpha oscillations conditionally on the age of the child. Using the proposed framework, we were able to gain novel information on the developmental trajectories of alpha oscillations for children with ASD and how the developmental trajectories differ between TD children and children with ASD.