Prediction intervals for neural network models using weighted asymmetric loss functions

We propose a simple and efficient approach to generate prediction intervals (PIs) for approximated and forecasted trends. Our method leverages a weighted asymmetric loss function to estimate the lower and upper bounds of the PIs, with the weights determined by the interval width. We provide a concise mathematical proof of the method, show how it can be extended to derive PIs for parametrised functions and argue why the method works for predicting PIs of dependent variables. The presented tests of the method on a real-world forecasting task using a neural network-based model show that it can produce reliable PIs in complex machine learning scenarios.Comment: 14 pages, 3 figures, not submitted anywhere ye

Resource allocation in a Quantum Key Distribution Network with LEO and GEO trusted-repeaters

International audienceQuantum Key Distribution (QKD) is a technology that enables the exchange of private encryption keys between two legitimate parties, using for this purpose different protocols that involve components of quantum mechanics. Since the rate at which secret keys can be exchanged depends on the attenuation that the optical signals experience, it is convenient to replace terrestrial fibers with optical satellite links to implement a QKD network at a global scale. Then, satellite nodes can take the role of trusted-relays, forwarding the secret keys from the sources to the destinations. However, since the rate at which secret keys can be generated in each quantum link is limited, it is very important to select the intermediate satellite nodes to interconnect ground stations efficiently. This paper studies the most convenient allocation of resources in a QKD network that combines both GEO and LEO satellites, which provide complementary services according to their position in the sky. The aim of the centralized routing algorithm is to select the most convenient trusted-relays to forward the secret keys between pairs of ground stations, verifying the constraints that satelliteto-ground and inter-satellite quantum channels have in practice