Maximal Correlation

Maximal correlation quantifies the strongest possible linear relationship between two random variables or processes, aiming to uncover hidden dependencies and improve data analysis. Current research focuses on developing algorithms, such as the Functional Maximal Correlation Algorithm (FMCA) and variations of Canonical Correlation Analysis (CCA), to efficiently estimate maximal correlation in diverse settings, including high-dimensional data and hierarchical structures like image hierarchies and graph embeddings. These advancements are impacting fields like transfer learning, where maximal correlation helps optimize the combination of multiple data sources, and dimensionality reduction, where it enables structure-aware feature extraction. The resulting improved feature representations and enhanced model performance have broad implications across machine learning and data analysis.