A1333
Title: Reduced-rank generalized tensor-on-tensor regression
Authors: Carlos Llosa - Sandia National Laboratories (United States) [presenting]
Daniel M Dunlavy - Sandia National Laboratories (United States)
Richard B Lehoucq - Sandia National Laboratories (United States)
Jeremy Myers - Sandia National Laboratories (United States)
Tian Ma - Sandia National Laboratories (United States)
Abstract: The Generalized Tensor-on-Tensor Regression Model (GToTR) is introduced as a novel modeling framework that extends the Generalized Linear Model (GLM) and Tensor-on-Tensor Regression (ToTR) for Regression problems involving tensor data, that is, multidimensional arrays. As with GLMs, GToTR allows a Linear Model to relate expected responses to covariates via a link function, providing flexibility in solving problems beyond typical identity link/Gaussian-response Regression. Similarly, as in ToTR, GToTR allows for tensor covariates and responses by leveraging their tensor structure that is often discarded when the data is vectorized and modeled entry-wise using scalar-response GLMs. GToTR combines both approaches, thus making parameter inference possible in situations where a large sample size would otherwise be necessary for a well-posed inference problem. Instead of requiring large samples, low-rank tensor structure is imposed on the GToTR parameter tensor, leading to a well-posed inference problem. An algorithmic framework for solving the GToTR inference problem is introduced when the Canonical Polyadic (CP) low-rank structure is imposed on the GToTR parameter tensor, and multiple applications of GToTR are illustrated on simulated and real-world data.
