We study the fundamental limits to the expressive power of neural networks. Given two sets F, G of real-valued functions, we first prove a general lower bound on how well functions in F can be approximated in Lp(μ) norm by functions in G, for any p≥1 and any probability measure μ. The lower bound depends on the packing number of F, the range of F, and the fat-shattering dimension of G. We then...
In animal genetics, linear mixed models are pivotal in determining the genetic and environmental impacts on animal traits, which is critical for designing effective breeding strategies. Traditional approaches, such as restricted maximum likelihood, rely on the assumption of multi-normality in trait distributions. However, this assumption often fails in practice due to the non-Gaussian nature...
Recently, one-dimensional Poincaré inequalities were used in Global Sensitivity Analysis (GSA) to provide upper bounds and chaos-type approximations of Sobol indices with derivative-based global sensitivity measures. As a new proposal, we develop the use of one-dimensional weighted Poincaré inequalities. The use of weights provides an additional degree of freedom that can be manipulated to...
La médecine de précision permet aux patients atteints de maladies
chroniques (diabètes, cancer…) de mettre au centre leurs propres
informations afin d'améliorer leur santé. Les stratégies de
traitements adaptatifs ou "Dynamic Treatment Regimes" sont une branche
de ce domaine médical. Elles établissent une règle de décision à
chaque étape du processus de guérison, en se basant sur...
Présentation de métamodèles pour le code de calcul DRACCAR qui simule le phénomène de renoyage du coeur d'un réacteur nucléaire.
Differential gene expression studies aim to identify genes whose mean expression level differs significantly between two known populations. The state-of-the-art approach to this problem consists of performing one test per gene, followed by a multiple testing correction in order to control the False Discovery Rate (FDR), which is the expected proportion of errors among selected genes. The...
