B1795
Title: Jointly modeling and clustering tensors in high dimensions
Authors: Biao Cai - City University of Hong Kong (United States) [presenting]
Abstract: The problem of jointly modeling and clustering populations of tensors is considered by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, plausible dimension reduction assumptions are employed that exploit the intrinsic structures of tensors such as low-rankness in the mean and separability in the covariance. In estimation, an efficient high-dimensional expectation-conditional-maximization (HECM) algorithm is developed that breaks the intractable optimization in the M-step into a sequence of much simpler conditional optimization problems, each of which is convex, admits regularization and has closed-form updating formulas. The theoretical analysis is challenged by both the non-convexity in the EM-type estimation and having access to only the solutions of conditional maximizations in the M-step, leading to the notion of dual non-convexity. It is demonstrated that the proposed HECM algorithm, with an appropriate initialization, converges geometrically to a neighborhood that is within the statistical precision of the true parameter. The efficacy of the proposed method is demonstrated through comparative numerical experiments and an application to a medical study, where the proposal achieves an improved clustering accuracy over existing benchmarking methods.
