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

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

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

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

Clinical characteristics of 80 subjects with KCNQ2-related encephalopathy: Results from a family-driven survey

Variants of KCNQ2 are associated with a wide spectrum of disorders, ranging from Self-limiting Neonatal Epilepsy (SelNE) to Early Onset Developmental and Epileptic Encephalopathy (KCNQ2-DEE). Comorbidities associated with this end of the spectrum have been seldomly described and their impact on the life of patients and their families is yet to be investigated. Collaborating with caregivers from different European family associations, we have developed a questionnaire aimed at investigating the onset and frequency of epileptic seizures, anti-seizure medications (ASM), hospitalizations, stages of development, and comorbidities. Responses from 80 patients, 40 males, from 14 countries have been collected. Median age 7.6 years (4 months - 43.6 years). Of 76 epileptic patients (93.6%), 55.3% were seizure-free with a mean age at last seizure of 26.7 months. Among patients with active epilepsy, those older have a lower frequency of seizures (p > 0.05). We were able to identify three different clusters of varying severity (Mild, Severe, Profound), based on neurodevelopmental features and symptoms, excluding epilepsy. Patients in a higher severity cluster had a higher mean number of comorbidities, which had a higher impact on families. Notably, patients in different clusters presented different epilepsy onset and courses. This study constitutes the most extensive data collection of patients with KCNQ2-DEE, with a focus on comorbidities in a wide age group. The participation of caregivers helps to define the impact of the disease on the lives of patients and families and can help identify new primary and secondary outcomes beyond seizures in future studies

p.Ala541Thr variant of MEN1 gene: A non deleterious polymorphism or a pathogenic mutation?

Context Multiple Endocrine Neoplasia Type 1 (MEN1) is an autosomal dominant inherited syndrome, related to mutations in the MEN1 gene. Controversial data suggest that the nonsynonymous p.Ala541Thr variant, usually considered as a non-pathogenic polymorphism, may be associated with an increased risk of MEN1-related lesions in carriers. Objective The aim of this study was to evaluate the pathogenic influence of the p.Ala541Thr variant on clinical and functional outcomes. Patients and methods We analysed a series of 55 index patients carrying the p.Ala541Thr variant. Their clinical profile was compared to that of 117 MEN1 patients. The biological impact of the p.Ala541Thr variant on cell growth was additionally investigated on menin-deficient Leydig cell tumour (LCT)10 cells generated from Men1+/Men1− heterozygous knock-out mice, and compared with wild type (WT). Results The mean age at first appearance of endocrine lesions was similar in both p.Ala541Thr carriers and MEN1 patients, but no p.Ala541Thr patient had more than one cardinal MEN1 lesion at initial diagnosis. A second MEN1 lesion was diagnosed in 13% of MEN1 patients and in 7% of p.Ala541Thr carriers in the year following preliminary diagnosis. Functional studies on LCT10 cells showed that overexpression of the p.Ala541Thr variant did not inhibit cell growth, which is in direct contrast to results obtained from investigation of WT menin protein. Conclusion Taken together, these data raise the question of a potential pathogenicity of the p.Ala541Thr missense variant of menin that commonly occurs within the general population. Additional studies are required to investigate whether it may be involved in a low-penetrance MEN1 phenotype

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

Lessons from prospective longitudinal follow-up of a French APECED cohort

Background Autoimmune polyendocrinopathy-candidiasis-ectodermal dystrophy syndrome is a rare disease caused by biallelic mutations of the AIRE gene, usually presenting with the triad hypoparathyroidism-adrenal failure-chronic mucocutaneous candidiasis (CMC) and nonendocrine manifestations. The aim of this study was to determine the molecular profile of the AIRE gene, the prevalence of rare manifestations, and to characterize immunological disturbances in a French cohort. Patients and Methods A national, multicenter prospective observational study to collect genetic, clinical, biological, and immunological data (NCT03751683). Results Twenty-five patients (23 families) were enrolled. Eleven distinct AIRE variants were identified, 2 of which were not previously reported: an intronic variant, c.653-70G > A, and a c.1066del (p.Arg356GlyfsX22) variant (exon 9). The most common was the Finnish variant c.769C > T (16 alleles), followed by the variant c.967_979del13 (15 alleles), which seemed associated with a less severe phenotype. Seventeen out of 25 patients were homozygote. The median number of clinical manifestations was 7; 19/25 patients presented with the hypoparathyroidism-adrenal failure-CMC triad, 8/13 showed pulmonary involvement, 20/25 had ectodermal dystrophy, 8/25 had malabsorption, and 6/23 had asplenia. Fifteen out of 19 patients had natural killer cell lymphopenia with an increase in CD4+ and CD8+ T lymphocytes and an age-dependent alteration of B lymphocyte homeostasis compared with matched controls (P < .001), related to the severity of the disease. All tested sera (n = 18) were positive for anti-interferon-α, 15/18 for anti-IL-22 antibodies, and 13/18 for anti-IL-17F antibodies, without clear phenotypic correlation other than with CMC. Conclusion This first prospective cohort showed a high AIRE genotype variability, with 2 new gene variants. The prevalence of potentially life-threatening nonendocrine manifestations was higher with systematic screening. These manifestations could, along with age-dependent B-cell lymphopenia, contribute to disease severity. Systematic screening for all the manifestations of the syndrome would allow earlier diagnosis, supporting vaccination and targeted therapeutic approaches