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Explore the intersection of statistical learning and tensor analysis in this comprehensive tutorial that addresses two critical areas of modern data science. Learn about synthetic data methods for handling imbalanced classification problems where positive class samples represent only a small fraction of the dataset, and discover how to overcome the challenges of models being dominated by majority classes. Examine the systematic bias that synthetic augmentation can introduce, understand mitigation strategies, and determine optimal amounts of synthetic data for effective learning. Delve into high-dimensional tensor data analysis, focusing on large-scale arrays with three or more modes that appear in biomedical science, network analysis, and financial econometrics. Master the unique statistical and computational challenges these data types present, including why classical matrix methods fail to extend directly and how vectorization can destroy multiway structure. Understand the NP-hard nature of basic tensor operations and explore new algorithmic and theoretical tools developed to address these challenges. Gain insights into recent advances in tensor-based methodology and theory, covering representation and low-rank structure, dimension reduction, regression, and clustering techniques. Analyze the statistical computational trade-offs that are unique to high-dimensional tensor settings and not present in lower-order data structures.
