A0726
Title: Depth meets machine learning: Kernel mean embeddings in functional data analysis
Authors: Stanislav Nagy - Charles University (Czech Republic) [presenting]
George Wynne - University of Bristol (United Kingdom)
Abstract: Statistical depths are a toolbox of methods that introduce elements of nonparametric statistics to multivariate or more complex data. The h-depth is a relatively simple yet well-performing common depth used in functional data analysis. It is shown that h-depth can be interpreted as a kernel mean embedding, well known in statistical machine learning. This facilitates answers to several open questions regarding the statistical properties of functional depths. It is shown that (i) h-depth is inherently a kernel-based method; (ii) several h-depths possess explicit expressions without the need to estimate them using Monte Carlo procedures; (iii) under minimal assumptions, h-depths and their maximizers are uniformly strongly consistent and asymptotically Gaussian; and (iv) several h-depths uniquely characterize probability distributions in separable Hilbert spaces. In addition, a link is also provided between the depth and empirical characteristic function-based procedures for functional data.
