B0841
Title: Approximate computation of data depths that satisfy the projection property
Authors: Rainer Dyckerhoff - University of Cologne (Germany) [presenting]
Pavlo Mozharovskyi - CREST-ENSAI (France)
Abstract: Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $R^d$. If the depth of a point can be represented as the minimum of the depths with respect to all unidimensional projections of the data, then the depth satisfies the so-called projection property. Such depths form an important class that includes many of the depths that have been proposed in literature. For depths that satisfy the projection property an approximate algorithm can easily be constructed since taking the minimum of the depths with respect to only a finite number of unidimensional projections yields an upper bound for the depth with respect to the multivariate data. Such an algorithm is particularly useful if no exact algorithm exists or if the exact algorithm has a high computational complexity, as is the case with the halfspace depth or the projection depth. To compute these depths in high dimensions, the use of an approximate algorithm with better complexity is surely preferable. Several strategies for selecting the univariate projections are proposed and the performances of the respective algorithms are compared.
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