Sparse Statistical Models for High-Dimensional Data

: (Alternative Format Thesis)

Abstract

This thesis explores statistical methods for high-dimensional data and will be composed of twomain parts.The first part of the thesis attempts to introduce a proposed low-rank pre-smoothing methodwithin the framework of a conventional multivariate linear regression model. In this context,we establish theoretical results that demonstrate the effectiveness of the new methodology. Tofurther validate its performance, a series of simulated experiments are conducted, where weempirically quantify the benefits and improvements our approach offers over existing methods.Additionally, from the environmental sciences and genetic expression studies, we evaluate ourtechnique to demonstrate its practical applicability in handling complex data structures.Subsequently, we extend the proposed method to incorporate regularisation, with a focus onridge regression to address challenges arising from high-dimensional settings and multicollinearity.By applying ridge regression within the multivariate linear framework, we enhance the robustnessof our method. Through a set of controlled simulations, we assess the performance of theregularised model under varying conditions.We further adapt our method to account for temporal dependencies by adapting it to multivariate time series data, with a specific focus on applications in neuroscience. To demonstrateits practical utility, we apply the method to functional magnetic resonance imaging data andcompare its performance with existing approaches in the field. This application underscoresthe flexibility of our framework in addressing domain-specific challenges posed by structuredtemporal data in neuroscience.The second part of the thesis, specifically Chapter 6 focuses on applied research in camerafingerprint detection, based on the work conducted during the internship with the companyCameraForensics. This section explores practical techniques for identifying camera source fingerprints, leveraging wavelet decomposition for image analysis. Through extensive experiments,we evaluate the effectiveness of these techniques in real-world scenarios.

Date of Award	22 Apr 2026
Original language	English
Awarding Institution	University of Bath
Supervisor	Sandipan Roy (Supervisor) & Matthew Nunes (Supervisor)