The design of a metric between probability distributions is a longstanding problem motivated
by numerous applications in Machine Learning. Focusing on continuous probability …

Statistical depth functions are a standard tool in nonparametric statistics to extend order-
based univariate methods to the multivariate setting. Since there is no universally accepted …

The recently defined concept of statistical depth function for fuzzy sets provides a theoretical
framework for ordering fuzzy sets with respect to the distribution of a fuzzy random variable …

For a mixed-type dataset, we propose a new procedure to assess the quality of an
observation as a central tendency. Next, we apply this technique to valuate the functional …

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 …

This paper introduces several depths for random sets with possibly non-convex realisations,
proposes ways to estimate the depths based on the samples and compares them with …

The Supplement contains proofs and auxiliary results, additional simulations for the two-
sample test, additional simulations for distance profiles and transport ranks for multimodal …

In this paper we present the methodology for detecting outliers and testing the goodness-of-
fit of random sets using topological data analysis. We construct the filtration from level sets of …

This paper introduces several depths for random sets with possibly non-convex realisations,
proposes ways to estimate the depths based on the samples and compares them with …

We study a statistical data depth with respect to compact convex random sets, which is
consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In addition, it …