Adaptive estimation in circular functional linear models

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an orthogonal series estimator of the slope function, by replacing the first m theoretical coefficients of its development in the trigonometric basis by adequate estimators. Wepropose a model selection procedure for m in a set of admissible values, by defining a contrast function minimized by our estimator and a theoretical penalty function; this first step assumes the degree of ill posedness to be known. Then we generalize the procedure to a random set of admissible m's and a random penalty function. The resulting estimator is completely data driven and reaches automatically what is known to be the optimal minimax rate of convergence, in term of a general weighted L2-risk. This means that we provide adaptive estimators of both the slope function and its derivatives

Création automatique de classes de signatures manuscrites pour l'authentification en ligne

International audienceNous nous intéressons dans ce papier à l'optimisation d'un système d'authentification par signature manuscrite. Celui-ci est basé sur une approche Coarse To Fine et utilise l'algorithme Dynamic Time Warping ainsi qu'un seuil de décision global pour accepter ou rejeter un signataire. L'optimisation proposée réside dans l'utilisation d'un algorithme de classification non supervisée afin de déterminer automatiquement des classes de signatures. Pour chacune des classes, un seuil de décision spécifique est établi. Dans ces travaux, nous nous sommes plus particulièrement attaché à étudier l'impact de la classification sur les performance. Les résultats expérimentaux sur la base SVC montrent que l'on peut améliorer les performances en diminuant le taux d'erreur égale de 14,4%. Cependant la sensibilité de la classification est très grande et la notion de classe unique pour un signataire semble trop restrictive

CLT in Functional Linear Regression Models

International audienceWe propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology of the considered functional space. However, we show that we can get a CLT for the weak topology under mild hypotheses and in particular without assuming any strong assumptions on the decay of the eigenvalues of the covariance operator. Rates of convergence depend on the smoothness of the functional coefficient and on the point in which the prediction is made

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo. Compared to the standard Bayesian inference that suffers serious computational burden and unstableness for analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results as the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids where the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes.Comment: Under revie

Multiple functional regression with both discrete and continuous covariates

International audienceIn this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al. (2010a), the method, which support mixed discrete and continuous explanatory variables, is based on estimating a function-valued function in reproducing kernel Hilbert spaces by virtue of positive operator-valued kernels

Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account during the data analysis process. This is done by extending standard data analysis methods so that they can apply to functional inputs. A general way to achieve this goal is to compute projections of the functional data onto a finite dimensional sub-space of the functional space. The coordinates of the data on a basis of this sub-space provide standard vector representations of the functions. The obtained vectors can be processed by any standard method. In our previous work, this general approach has been used to define projection based Multilayer Perceptrons (MLPs) with functional inputs. We study in this paper important theoretical properties of the proposed model. We show in particular that MLPs with functional inputs are universal approximators: they can approximate to arbitrary accuracy any continuous mapping from a compact sub-space of a functional space to R. Moreover, we provide a consistency result that shows that any mapping from a functional space to R can be learned thanks to examples by a projection based MLP: the generalization mean square error of the MLP decreases to the smallest possible mean square error on the data when the number of examples goes to infinity

The Extracytoplasmic Domain of the Mycobacterium tuberculosis Ser/Thr Kinase PknB Binds Specific Muropeptides and Is Required for PknB Localization

The Mycobacterium tuberculosis Ser/Thr kinase PknB has been implicated in the regulation of cell growth and morphology in this organism. The extracytoplasmic domain of this membrane protein comprises four penicillin binding protein and Ser/Thr kinase associated (PASTA) domains, which are predicted to bind stem peptides of peptidoglycan. Using a comprehensive library of synthetic muropeptides, we demonstrate that the extracytoplasmic domain of PknB binds muropeptides in a manner dependent on the presence of specific amino acids at the second and third positions of the stem peptide, and on the presence of the sugar moiety N-acetylmuramic acid linked to the peptide. We further show that PknB localizes strongly to the mid-cell and also to the cell poles, and that the extracytoplasmic domain is required for PknB localization. In contrast to strong growth stimulation by conditioned medium, we observe no growth stimulation of M. tuberculosis by a synthetic muropeptide with high affinity for the PknB PASTAs. We do find a moderate effect of a high affinity peptide on resuscitation of dormant cells. While the PASTA domains of PknB may play a role in stimulating growth by binding exogenous peptidoglycan fragments, our data indicate that a major function of these domains is for proper PknB localization, likely through binding of peptidoglycan fragments produced locally at the mid-cell and the cell poles. These data suggest a model in which PknB is targeted to the sites of peptidoglycan turnover to regulate cell growth and cell division

Apnea of prematurity: from cause to treatment

Apnea of prematurity (AOP) is a common problem affecting premature infants, likely secondary to a “physiologic” immaturity of respiratory control that may be exacerbated by neonatal disease. These include altered ventilatory responses to hypoxia, hypercapnia, and altered sleep states, while the roles of gastroesophageal reflux and anemia remain controversial. Standard clinical management of the obstructive subtype of AOP includes prone positioning and continuous positive or nasal intermittent positive pressure ventilation to prevent pharyngeal collapse and alveolar atelectasis, while methylxanthine therapy is a mainstay of treatment of central apnea by stimulating the central nervous system and respiratory muscle function. Other therapies, including kangaroo care, red blood cell transfusions, and CO2 inhalation, require further study. The physiology and pathophysiology behind AOP are discussed, including the laryngeal chemoreflex and sensitivity to inhibitory neurotransmitters, as are the mechanisms by which different therapies may work and the potential long-term neurodevelopmental consequences of AOP and its treatment