Keywords

Sparse Kronecker Product, Image Regression, High-Dimensional Data, Tensor Decomposition

Abstract

Understanding which features drive the outputs of modern learning systems remains a core challenge for regression and classification. While deep neural networks can be highly accurate, their latent representations often obscure how inputs map to decisions, limiting statistical inference, stakeholder trust, and practical use in domain decision-making. Sparse Kronecker Product Decomposition (SKPD) is a frequentist, tensor-structured approach that offers interpretable regression/classification in high dimensions. However, standard SKPD restricts relationships among predictors and covariates and is typically limited to order-2 tensors. This dissertation introduces E-CSKPD, an ensemble framework that (i) revisualizes designs to control non-imaging covariates; (ii) applies invertible, CNN-inspired transforms that improve conditioning and enable exact back-mapping for inference; (iii) generalizes naturally to higher-order tensors; and (iv) aggregates slice/ROI models with a transparent meta-learner to capture nonlinearities while preserving statistical interpretability. Theoretical results establish estimation consistency and linear convergence of the alternating-minimization algorithm up to the statistical precision limit determined by sample size and model complexity.

Completion Date

2025

Semester

Fall

Committee Chair

Huang, Hsin-Hsiung

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Statistics & Data Science

Format

PDF

Identifier

DP0029765

Document Type

Thesis

Campus Location

Orlando (Main) Campus

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