Methodological advancements in high-dimensional sparse-group models
File(s)
Author(s)
Feser, Fabio
Type
Thesis
Abstract
This thesis develops novel sparse-group methodologies for high-dimensional data analysis, with a particular emphasis on genetic applications. Genes naturally form in groups, and utilising this inherent grouping structure can substantially enhance model performance. Traditional group-only models often perform poorly due to the inclusion of noise variables within active groups. Sparse-group models address this limitation by introducing additional sparsity within groups. Moreover, effective control of the false discovery rate (FDR) is crucial, as it supports cost-efficient validation of findings.
The main methodological contribution of this thesis is the Sparse-group SLOPE (SGS) model. The SGS framework achieves FDR control at both the group and variable levels, allowing it to outperform competitive methods in disease prediction. To improve the computational efficiency of SGS, a new sparse-group strong
screening framework is introduced, which performs two layers of screening. It is applied to both SGS and group SLOPE (gSLOPE), substantially reducing runtime by excluding inactive features before optimisation, without compromising solution optimality. This framework is also extended to the Sparse-group Lasso (SGL) and adaptive SGL models using the Dual Feature Reduction (DFR) method, with our empirical results establishing it as the state-of-the-art screening approach for SGL. Further, this thesis tackles the problem of model selection for SLOPE models under general settings by developing Bayesian formulations of gSLOPE and SGS. The models employ spike-and-slab priors, providing simultaneous estimation of noise and model parameters, uncertainty quantification, and adaptivity to underlying sparsity structures. A two-step procedure and a scaled regression approach are also proposed for SLOPE models. Empirical studies demonstrate that the proposed Bayesian methods provide the optimal implementation of SLOPE under general settings, achieving reliable FDR control across a wide range of scenarios and demonstrating superior power and predictive performance compared to existing approaches.
The main methodological contribution of this thesis is the Sparse-group SLOPE (SGS) model. The SGS framework achieves FDR control at both the group and variable levels, allowing it to outperform competitive methods in disease prediction. To improve the computational efficiency of SGS, a new sparse-group strong
screening framework is introduced, which performs two layers of screening. It is applied to both SGS and group SLOPE (gSLOPE), substantially reducing runtime by excluding inactive features before optimisation, without compromising solution optimality. This framework is also extended to the Sparse-group Lasso (SGL) and adaptive SGL models using the Dual Feature Reduction (DFR) method, with our empirical results establishing it as the state-of-the-art screening approach for SGL. Further, this thesis tackles the problem of model selection for SLOPE models under general settings by developing Bayesian formulations of gSLOPE and SGS. The models employ spike-and-slab priors, providing simultaneous estimation of noise and model parameters, uncertainty quantification, and adaptivity to underlying sparsity structures. A two-step procedure and a scaled regression approach are also proposed for SLOPE models. Empirical studies demonstrate that the proposed Bayesian methods provide the optimal implementation of SLOPE under general settings, achieving reliable FDR control across a wide range of scenarios and demonstrating superior power and predictive performance compared to existing approaches.
Version
Open Access
Date Issued
2025-11-12
Date Awarded
2026-04-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Evangelou, Marina
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
2602754
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)