TENSOR DIMENSION REDUCTION METHODS FOR MODELING HIGH DIMENSIONAL SPATIO-TEMPORAL DATA

Author

Rukayya Ibrahim, Southern Illinois University CarbondaleFollow

Date of Award

8-1-2022

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Samadi, Yaser

Abstract

Data observed simultaneously in both space and time are becoming increasingly prevalent with applications in diverse areas, from ecology to financial econometrics. The datasets are massive with several variables observed in varying locations and time and are often accompanied with irregularities. Therefore, there is need to formulate efficient models that can efficiently handle the size and all dependencies of massive datatsets while performing predictions and forecast well. In this work, we propose a new model for matrix-valued spatio-temporal data using the classic vector autoregressive (VAR) model on each column (location) of the matrix. This allows us to present the coefficient matrices in a unified format. To achieve dimension reduction, we decompose the folded coefficient matrix using tensor decomposition, which allows us to have reduced dimension in four directions which automatically not only reduces the number of model parameters significantly but also achieves substantial efficiency gains. We propose an alternating least squares algorithm to estimate the parameters of interest and derive the asymptotic properties of the proposed estimators for low dimension. For high dimensional setting, we propose a sparsity-inducing norms using regularized estimation techniques. An alternating least squares algorithm with sparsity inducing norms is presented. We present simulation results and a real data analysis to demonstrate the superiority of our estimators.