Functional Mixed Membership Models
提出一种贝叶斯函数型混合成员模型，利用多元Karhunen-Loève定理实现高斯过程的可扩展表示，并建立条件后验一致性，适用于脑电图等函数型数据，可解释均值和协方差结构。
Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this paper, we propose a Bayesian mixed membership model for functional data. By using the multivariate Karhunen-Loève theorem, we are able to derive a scalable representation of Gaussian processes that maintains 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 mixed membership models, our proposal allows for increased modeling flexibility, with the benefit of a directly interpretable 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 proportions. Supplementary materials, including proofs, are available online. The R package BayesFMMM is available to fit functional mixed membership models.