Advances in Statistical Machine Learning for Tensors: Parametric and Non-Parametric Approaches

Music City Center 

High-order tensor datasets present unique challenges in recommendation systems, neuroimaging, and social networks. In this talk, we discuss our recent advancements in developing statistical models, efficient algorithms, and data-driven solutions to address high-dimensional tensor problems. Specifically, we introduce two key approaches: parametric tensor block models for higher-order clustering and nonparametric latent variable models for tensor denoising. We establish both statistical and computational guarantees for each method. Polynomial-time algorithms are developed with proven efficiency. The practical utility of our methods is demonstrated through neuroimaging data application and social network studies.

Higher-order tensors, high-dimensional statistics, statistical-computational efficiency, parametric, non-parametric, clustering, denoising,