B1160
Title: A spectral method for identifiable grade of membership analysis in high dimensions
Authors: Yuqi Gu - Columbia University (United States) [presenting]
Ling Chen - Columbia University (United States)
Abstract: Grade of Membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore GoM models have a richer modeling capacity than the latent class model that restricts each subject to belong to a single profile. The flexibility of GoM comes at the cost of more challenging identifiability and estimation problems. A singular value decomposition (SVD) based spectral approach is proposed for GoM analysis. The approach is based on the observation that the expectation of the data matrix has a low-rank decomposition under a GoM model. For identifiability, sufficient and almost necessary conditions are developed for a notion of expectation identifiability. For estimation, only a few leading singular vectors of the observed data matrix are extracted, and the simplex geometry of these vectors is exploited to estimate the mixed membership scores. The spectral method has a huge computational advantage over Bayesian or likelihood-based methods and is scalable to large-scale and high-dimensional data. Furthermore, singular subspace perturbation theory is leveraged to establish entry-wise consistency and estimation error bounds for parameters in the high-dimensional setting. Extensive simulation studies demonstrate the superior efficiency and accuracy of the method compared to its competitors. The method of applying it to a personality test dataset is illustrated.
