Statistics & Data Science GIDP, Ph.D. Candidate
When
10 a.m. – Noon, April 8, 2026
Where
https://arizona.zoom.us/j/82786314286
Title: Sparse and Smooth Estimation in High-Dimensional Structured Regression
Abstract: This dissertation develops new methods and theory for high-dimensional structured regression, focusing on models that jointly promote sparsity and smoothness in functional estimates. Two problems are studied. First, we consider additive models, which represent multivariate functions as sums of univariate components, providing a flexible yet structured approach to modeling. The Component Selection and Smoothing Operator (COSSO) implements this idea within the smoothing spline ANOVA framework by penalizing the sum of component reproducing kernel Hilbert space (RKHS) norms, thereby inducing sparsity and smoothness through a single regularization term. However, its behavior under high-dimensional scaling remains unclear. We extend COSSO to high-dimensional settings by developing a computationally efficient algorithm and establishing non-asymptotic guarantees for estimation accuracy. Second, we study scalar-on-image regression, which models the relationship between a scalar response and an image through a bivariate coefficient function. Existing approaches often emphasize smoothness, which can limit interpretability when only localized regions are relevant. We introduce a Generalized Dantzig Selector framework that enforces both sparsity and smoothness, yielding interpretable spatial patterns by identifying non-influential regions and estimating continuous effects in regions with signal. We further establish non-asymptotic bounds for prediction and estimation error of the coefficient surface. The performance of both methods is validated through simulations and real data applications.
Zoom Link: https://arizona.zoom.us/j/82786314286