Choosing the most relevant level sets for depicting a sample of densities

Abstract

When exploring a sample composed with a set of bivariate density functions, the question of the visualisation of the data has to front with the choice of the relevant level set(s). The approach proposed in this paper consists in defining the optimal level set(s) as being the one(s) allowing for the best reconstitution of the whole density. A fully data-driven procedure is developed in order to estimate the link between the level set(s) and their corresponding density, to construct optimal level set(s) and to choose automatically the number of relevant level set(s). The method is based on recent advances in functional data analysis when both response and predictors are functional. After a wide description of the methodology, finite sample studies are presented (including both real and simulated data) while theoretical studies are reported to a final appendix.

Wasserstein gradients for the temporal evolution of probability distributions

“…Bolstad et al, 2003;Bigot et al, 2017;Galichon, 2017;Cazelles et al, 2018;Bigot et al, 2019), and in visualization (e.g. Delicado and Vieu, 2017). In the one-dimensional case that we consider here, it is well known that the Wasserstein transport can also be expressed in terms of quantile functions (Hoeffding, 1940;Zhang and Müller, 2011;Chowdhury and Chaudhuri, 2019).…”

Wasserstein Gradients for the Temporal Evolution of Probability Distributions

“…Bolstad et al 2003;Bigot et al 2017a,b;Cazelles et al 2017;Galichon 2017), and in visualizations of distributions (e.g. Delicado and Vieu 2017). In the one-dimensional case that we consider here it is well known that the Wasserstein transport can also be expressed in terms of quantile functions (Hoeffding 1940;Zhang and Müller 2011;Chowdhury and Chaudhuri 2016).…”