Individualized Multilayer Tensor Learning with An Application in Imaging Analysis

• Activity Number: 482 - Statistical Methods in the Analysis of High-Order Structural Data with Possible Structural Changes
• Type: Invited
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Xiwei Tang* and Xuan Bi and Annie Qu
• Companies: University of Virginia and University of Minnesota and University of Illinois at Urbana-Champaign
• Keywords: Multidimensional data; Spatial correlation; Tensor decomposition; Dimension reduction; Imaging processing

Abstract

This work is motivated by multimodality breast cancer imaging data, which is quite challenging in that the signals of discrete tumorassociated microvesicles (TMVs) are randomly distributed with heterogeneous patterns. This imposes a significant challenge for conventional imaging regression and dimension reduction models assuming a homogeneous feature structure. We develop an innovative multilayer tensor learning method to incorporate heterogeneity to a higher-order tensor decomposition and predict disease status effectively through utilizing subject-wise imaging features and multimodality information. Specifically, we construct a multilayer decomposition which leverages an individualized imaging layer in addition to a modality-specific tensor structure. To achieve scalable computing, we develop a new bi-level block improvement algorithm. In theory, we investigate both the algorithm convergence property, tensor signal recovery error bound and asymptotic consistency for prediction model estimation. We also apply the proposed method for simulated and human breast cancer imaging data, demonstrating that the proposed method outperforms other competing methods.