Philippe Jacquet

Geoffrey Deperle, Christine Fricker, Philippe Jacquet et al.

We study the asymptotic behaviour of the distance to the first available parking slot in a recursive Manhattan street network endowed with a hyperfractal intensity structure, where slot-release events occur according to Poisson processes along the streets. We establish, by analysing the associated self-similar harmonic sums via Mellin-transform asymptotics, a power-law decay of the expected distance as the total intensity grows, with exponent equal to the inverse of the hyperfractal dimension. In particular, the scaling exponent depends only on the large-scale geometry of the network. We further prove that this exponent is robust under random multiplicative modulations of the street intensities: mild stochastic heterogeneity affects only the multiplicative constant. Similar scaling behaviour holds for the variance, the number of turns before parking, and for a jump-over variant of the search strategy.

Federico Amato, Fabian Guignard, Philippe Jacquet et al.

The presence of irrelevant features in the input dataset tends to reduce the interpretability and predictive quality of machine learning models. Therefore, the development of feature selection methods to recognize irrelevant features is a crucial topic in machine learning. Here we show how the General Regression Neural Network used with an anisotropic Gaussian Kernel can be used to perform feature selection. A number of numerical experiments are conducted using simulated data to study the robustness of the proposed methodology and its sensitivity to sample size. Finally, a comparison with four other feature selection methods is performed on several real world datasets.