Carlos Llosa "Low-Rank Generalized Tensor-on-Tensor Regression and Applications"
- Sponsor
- Coordinated Science Lab
- Speaker
- Carlos Llosa
- Originating Calendar
- CSL SINE Group
MONDAY, MARCH 2ND – 4:00-5:00PM -
LOCATION: CSL 141
Speaker: Carlos Llosa, Research And Development Statistician (Senior Member of Technical Staff) in Statistical Sciences at Sandia National Laboratories
Title: Low-Rank Generalized Tensor-on-Tensor Regression and Applications
Abstract: We introduce the Generalized Tensor-on-Tensor Regression model (GToTR), a novel modeling framework that extends the Generalized Linear Model (GLM) and Tensoron-Tensor Regression (ToTR) for regression problems involving tensor data, i.e., multidimensional arrays. As with GLMs, GToTR allow 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, GToTRs allow 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, we impose low-rank tensor structure on the GToTR parameter tensor, thus requiring fewer samples, and leading to a well-posed inference problem. Here, we extend GLM and ToTR to GToTR, introduce an algorithmic framework for solving the GToTR inference problem when the Canonical Polyadic (CP) low-rank structure is imposed on the GToTR parameter tensor, and illustrate multiple uses of GToTRs on simulated and real-world application data.
This is joint work Daniel M. Dunlavy, Richard B. Lehoucq and Tian J. Ma of SandiaNational Laboratories, and Jeremy Myers. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutionsof Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for theU.S. Department of Energy’s National Nuclear Security Administration under contractDE-NA0003525
Biography: Carlos obtained his M.S. and Ph.D. degrees in Statistics from Iowa State University in 2018 and 2022, respectively, and received the B.S. degree in Mathematics from The University of Arizona in 2015. The doctoral dissertation was advised by Ranjan Maitra on the statistical analysis of tensor-valued data. Currently, he is a Senior Member of the Technical Staff at the Department of Statistical Sciences at Sandia National Laboratories in Albuquerque, NM. Also an associate editor for Sankhya B, The Indian Journal of Statistics.
His main interest lies in the area of multilinear statistics, or the statistical analysis of tensor-valued data. This involves creating new models for tensor data, and also studying existing tensor models from a statistical perspective. More generally, he is interested in the statistical analysis of complex data structures, including functional, spatial, temporal, and tensor-variate data, particularly at the intersections of two or more of these domains.We hope you can make it!