Explainable and Robust AI for Medical Applications
Open Access DepositedIn recent years, the rapid expansion of data-intensive disciplines has necessitated the development of robust statistical methodologies capable of addressing the challenges posed by high-dimensional and complex data . This dissertation investigates critical issues in statistical inference and robust estimation, proposing innovative methodologies that bridge theoretical rigor with practical applications across various domains. By evaluating the limitations of conventional methods—especially under scenarios of heavy-tailed distributions, model misspecification, and the presence of outliers—this work lays the groundwork for more reliable and interpretable data analysis tools . The study begins with an extensive review of existing literature on high-dimensional inference, robust estimation techniques, and regularization strategies . Motivated by the challenges that arise when traditional methods are applied to modern datasets, we introduce a novel estimation framework that combines robust loss functions with adaptive regularization. This framework is designed to mitigate the adverse effects of non-Gaussian errors and anomalous observations while ensuring both statistical efficiency and model sparsity . Central to this dissertation is the development of a new estimator that integrates state-of-the-art regularization techniques with robust statistical theory. We derive its asymptotic properties and establish conditions under which the estimator is consistent and efficient, particularly in high-dimensional settings where the number of predictors may exceed the number of observations . Our approach demonstrates superior performance in variable selection by reliably identifying significant predictors while controlling for potential overfitting and noise. To address computational challenges, we propose an iterative optimization algorithm that efficiently solves the resulting non-convex problems, ensuring convergence even in complex scenarios . Extensive simulation studies are performed to benchmark our method against traditional approaches, revealing substantial improvements in bias reduction, variance stabilization, and predictive accuracy . These simulations highlight the estimator's resilience in the presence of data contamination and intricate correlation structures. The practical utility of the proposed methodology is further illustrated through applications in finance, bioinformatics, and social sciences. In each case, our method enhances model interpretability and provides more accurate predictions, thereby affirming its relevance across diverse research fields. Moreover, the integration of robust statistical methods with modern machine learning techniques is explored, offering enhanced reliability and interpretability in predictive models, particularly when handling noisy or incomplete datasets . Additional discussions in this dissertation address the theoretical underpinnings and practical implications of robust estimation in high-dimensional frameworks. We examine the trade-offs between robustness and efficiency, offering guidelines for practitioners on balancing these aspects in real-world applications . Furthermore, potential extensions of the proposed methods are considered, including their adaptation to dynamic data environments and emerging applications in network analysis and time-series forecasting . Overall, the contributions of this work are multifaceted. By developing a comprehensive framework that addresses both theoretical and computational challenges, this dissertation advances robust statistical estimation, improves model accuracy, and enhances interpretability. The insights gained have significant implications for statistical theory and practical applications alike, paving the way for innovative interdisciplinary research in the era of big data. The methodologies and findings presented herein not only contribute to a deeper understanding of robust estimation but also serve as a solid foundation for future developments in the field.
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