A framework for high-dimensional tensor regression models with dependence

• Activity Number: 111
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Garvesh Raskutti* and Ming Yuan
• Companies: University of Wisconsin and University of Wisconsin - Madison
• Keywords: Functional data ; additive models ; convex program

Abstract

Large-scale tensor regression problems are arising in more and more applications in science. Statistical models such as multi-response regression, vector auto-regressive problems and many others can be formulated as tensor regression models. When the dimension of the tensor is large, low-dimensional structure such as sparsity or low-rank need to be imposed. In this talk, I present a framework that yields general upper bounds using convex methods and lower bounds for high-dimensional tensor problems assuming the underlying tensor has low-dimensional structure based on matriculation. Our results yield optimal bounds in a number of settings in which the covariates may be dependent (e.g. auto-regressive models).