A unified high-dimensional statistical learning framework for functional data analysis and spatio-temporal modeling in complex systems

Abstract

 The increasing availability of high-dimensional and complex datasets in contemporary applications demands efficient and unified statistical learning methodologies. This study introduces a comprehensive high-dimensional framework that combines dimensionality reduction, functional data analysis (FDA), and spatio-temporal modeling to effectively handle challenges associated with complex system data. The framework utilizes sparsity-based methods to address high dimensionality, functional representations to model continuous data characteristics, and spatio-temporal techniques to capture evolving dependencies across space and time. It enhances interpretability, robustness, and predictive accuracy while maintaining computational efficiency for large-scale problems. The versatility of the framework is demonstrated through its applicability across multiple domains, offering a reliable foundation for analyzing high-dimensional functional and spatio-temporal datasets.