Covariate Adjusted Functional Mixed Membership Models.

Area of Science:

• Statistics
• Machine Learning
• Neuroscience

Background:

• Mixed membership models offer flexibility in unsupervised learning, allowing partial data belonging to multiple clusters.
• Functional data analysis extends these models to handle data with inherent sequential or spatial structures.
• Autism Spectrum Disorder (ASD) research often involves complex neuroimaging data, necessitating advanced analytical techniques.

Purpose of the Study:

• To extend functional mixed membership models to incorporate covariate-dependent structures.
• To ensure the identifiability of model parameters within the extended framework.
• To investigate developmental changes in brain activity (EEG alpha oscillations) in children with ASD.

Main Methods:

• Development of a multivariate Karhunen-Loève decomposition for scalable and flexible functional mixed membership models.
• Establishment of sufficient conditions for the identifiability of mean, covariance, and allocation structures.
• Application of the proposed framework to electroencephalography (EEG) data from children with and without ASD.

Main Results:

• The proposed framework provides a scalable and flexible approach for covariate-dependent functional mixed membership modeling.
• Identifiability conditions were established for the model's mean, covariance, and allocation components.
• Analysis of EEG data revealed significant differences in developmental changes of alpha oscillations between children with ASD and typically developing children.

Conclusions:

• The covariate-dependent functional mixed membership models offer novel insights into heterogeneous developmental trajectories.
• Individuals with ASD exhibit attenuated developmental changes in alpha oscillations compared to typically developing peers.
• This framework advances the analysis of complex functional neuroimaging data in developmental disorders.