Large-scale data depth: computation and applications – LS-Depth-CaP

Introduced by John Tukey, data depth measures centrality of an observation with respect to data. Being non-parametric, robust, and possessing attractive invariance properties, data depth substitutes density and quantiles in numerous applications. However, its large-scale applications are impeded by its computational infeasibility. LS-Depth-CaP project addresses this question in a systematic way. As the main objective, a link between statistical and computational properties of data depth should be established. Further, gradient-based optimization technique for smoothed data depth shall be developed with corresponding statistical guarantees. A Python library shall implement the obtained results. This will be used in applications: statistical analysis of the diffusion-tensor brain images and multivariate spectra of construction materials.