Statistical Depth

Statistical depth provides a framework for ranking multi-dimensional data points based on their centrality within a dataset, generalizing concepts like median and quantile to higher dimensions. Recent research focuses on developing new depth functions, such as those based on optimal control theory and eikonal equations, offering improved robustness and computational efficiency compared to traditional methods like Tukey depth. These advancements find applications in diverse fields, including natural language processing (e.g., analyzing text embeddings) and machine learning (e.g., enhancing differentially private linear regression), enabling more robust statistical analysis and inference in high-dimensional settings. The development of efficient algorithms for computing these depths is a key area of ongoing investigation.