arXiv subjects

Marco De Angelis

Publications and source records attributed to Marco De Angelis.

3 recordsLinked to original sources

arXiv2021

Why the 1-Wasserstein distance is the area between the two marginal CDFs

We elucidate why the 1-Wasserstein distance $W_1$ coincides with the area between the two marginal cumulative distribution functions (CDFs). We first describe the Wasserstein distance in terms of copulas, and then show that $W_1$ with the Euclidean distance is attained with the $M$ copula. Two random variables whose dependence is given by the $M$ copula manifest perfect (positive) dependence. If we express the random variables in terms of their CDFs, it is intuitive to see that the distance between two such random variables coincides with the area between the two CDFs.

math.ST↗

arXiv2021

The Creation of Puffin, the Automatic Uncertainty Compiler

An uncertainty compiler is a tool that automatically translates original computer source code lacking explicit uncertainty analysis into code containing appropriate uncertainty representations and uncertainty propagation algorithms. We have developed an prototype uncertainty compiler along with an associated object-oriented uncertainty language in the form of a stand-alone Python library. It handles the specifications of input uncertainties and inserts calls to intrusive uncertainty quantification algorithms in the library. The uncertainty compiler can apply intrusive uncertainty propagation methods to codes or parts of codes and therefore more comprehensively and flexibly address both epistemic and aleatory uncertainties.

cs.MS↗

arXiv2021

Interval propagation through the discrete Fourier transform

We present an algorithm for the forward propagation of intervals through the discrete Fourier transform. The algorithm yields best-possible bounds when computing the amplitude of the Fourier transform for real and complex valued sequences. We show that computing the exact bounds of the amplitude can be achieved with an exhaustive examination of all possible corners of the interval domain. However, because the number of corners increases exponentially with the number of intervals, such method is infeasible for large interval signals. We provide an algorithm that does not need such an exhaustive search, and show that the best possible bounds can be obtained propagating complex pairs only from the convex hull of endpoints at each term of the Fourier series. Because the convex hull is always tightly inscribed in the respective rigorous bounding box resulting from interval arithmetic, we conclude that the obtained bounds are guaranteed to enclose the true values.

eess.SP↗