Pic, Romain Dombry, Clément Naveau, Philippe Taillardat, Maxime

The theoretical advances on the properties of scoring rules over the past decades have broaden the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to improve the forecasts made by deterministic physical models. Numerous state-of-theart statistical postprocessing t...

Novello, Paul Poëtte, Gaël Lugato, David Congedo, Pietro

In the context of supervised learning of a function by a neural network, we claim and empirically verify that the neural network yields better results when the distribution of the data set focuses on regions where the function to learn is steep. We first traduce this assumption in a mathematically workable way using Taylor expansion and emphasize a...

Blain, Alexandre Thirion, Bertrand Neuvial, Pierre

Cluster-level inference procedures are widely used for brain mapping. These methods compare the size of clusters obtained by thresholding brain maps to an upper bound under the global null hypothesis, computed using Random Field Theory or permutations. However, the guarantees obtained by this type of inference - i.e. at least one voxel is truly act...

Nguyen, TrungTin Chamroukhi, Faicel Nguyen, Hien Duy Forbes, Florence

This study is devoted to the problem of model selection among a collection of Gaussian-gated localized mixtures of experts models characterized by the number of mixture components, and the complexity of Gaussian mean experts, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the...

Sarazin, Gabriel Marrel, Amandine da Veiga, Sébastien Chabridon, Vincent

L'apprentissage statistique dans le cas de données simulées par un code de calcul industriel, aussi appelé "métamodélisation", est une tâche dont la difficulté de mise en œuvre croît avec la dimension du problème et le manque de données d'apprentissage.Une analyse de sensibilité préliminaire peut venir en soutien de la construction du métamodèle po...

Forbes, Florence Nguyen, Hien Duy Nguyen, TrungTin Arbel, Julyan

A key ingredient in approximate Bayesian computation (ABC) procedures is the choice of a discrepancy that describes how different the simulated and observed data are, often based on a set of summary statistics when the data cannot be compared directly. Unless discrepancies and summaries are available from expert or prior knowledge, which seldom occ...

Durand, Amaury Roueff, François

In this paper, we review and clarify the construction of a spectral theory for weakly-stationary processes valued in a separable Hilbert space. We emphasize the link with functional analysis and provide thorough discussions on the different approaches leading to fundamental results on representations in the spectral domain. The clearest and most co...

Abeida, Habti Delmas, Jean-Pierre

This paper analyzes the deterministic (DCRB) and the stochastic (SCRB) Cram\'er-Rao bound on direction-of-arrival (DOA) estimation for twoequi-powered correlated complex circular or rectilinear sources affected by complex circular white noise in different complex elliptically symmetric (CES) data models.Beginning by decomposing these CRBs, into fac...

Nguyen, TrungTin Chamroukhi, Faicel Nguyen, Hien Duy McLachlan, Geoffrey

The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We establish and prove the following results: to an arbitrary degree of accuracy, (a) location-scale mixtures of a continuous probability density function (PDF) can approximate any continuous PDF, uniform...

Siviero, Emilia Chautru, Emilie Clémençon, Stéphan

In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory of statistical learning does not apply directly and guarantees of the generalization capacity of predictive r...