In statistical learning and analysis from shared data, which is increasingly widely adopted in
platforms such as federated learning and meta-learning, there are two major concerns …

For computing the exact value of the halfspace depth of a point wrt a data cloud of n points in
arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole …

Given data in R p, a Tukey κ-trimmed region is the set of all points that have at least Tukey
depth κ wrt the data. As they are visual, affine equivariant and robust, Tukey regions are …

We study depth measures for multivariate data defined by integrating univariate depth
measures, specifically, integrated dual (ID) depth introduced by Cuevas and Fraiman (2009) …

Simulated annealing is a widely used algorithm for the computation of global optimization
problems in computational chemistry and industrial engineering. However, global optimum …

Enthusiasm for Machine Learning is spreading to nearly all fields such as transportation,
energy, medicine, banking or insurance as the ubiquity of sensors through IoT makes more …

Algorithms are proposed for the computation of set-valued quantiles and the values of the
lower cone distribution function for bivariate data sets. These new objects make data …

Centrality on graphs aims at ranking vertices in terms of their contribution to facilitate the
communication flow in the network. Tukey depth is one of most widely used statistical …

The halfspace depth is a powerful tool for the nonparametric multivariate analysis. However,
its computation is very challenging for it involves the infimum over infinitely many directional …

We give robust recovery results for synchronization on the rotation group, SO (D). In
particular, we consider an adversarial corruption setting, where a limited percentage of the …