Appears in collection : New challenges in high-dimensional statistics / Statistique mathématique 2025

This tutorial brings together two rapidly developing topics in modern statistical learning: (i) synthetic data methods for imbalanced classification and (ii) high-dimensional tensor learning. In the first part, we focus on imbalanced data, where the positive class forms only a small fraction of the samples. Such imbalance makes classification challenging because models trained naively can be dominated by the majority class, leading to poor minority class performance. A widely used strategy is to generate synthetic minority samples and train classifiers on a mixture of observed and synthetic data. We discuss several key practical and theoretical questions in this area, including how synthetic augmentation can introduce systematic bias, how to mitigate that bias, and how to choose the amount of synthetic data needed for effective learning. In the second part, we turn to high-dimensional tensor data, large-scale arrays with three or more modes, that arise naturally in many fields such as biomedical science and networks, and financial econometrics. These data pose distinct statistical and computational challenges: classical matrix methods do not extend directly, vectorization can destroy multiway structure, and even basic tensor operations can be NP-hard, motivating new algorithmic and theoretical tools. We provide an overview of recent advances in censor-based methodology and theory, covering representation and low-rank structure, dimension reduction, regression, and clustering, along with statistical computational trade-offs that are not present in lower-order settings.