Resistant estimates for high dimensional and functional data based on random projections

We herein propose a new robust estimation method based on random projections that is adaptive and automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted contamination models, the procedure is robust and attains full efficiency. We tested the method using both simulated and real data.Fil: Fraiman, Jacob Ricardo. Universidad de San Andrés; Argentina. Universidad de la República; Uruguay. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Svarc, Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentin

An ANOVA approach for statistical comparisons of brain networks

The study of brain networks has developed extensively over the last couple of decades. By contrast, techniques for the statistical analysis of these networks are less developed. In this paper, we focus on the statistical comparison of brain networks in a nonparametric framework and discuss the associated detection and identification problems. We tested network differences between groups with an analysis of variance (ANOVA) test we developed specifically for networks. We also propose and analyse the behaviour of a new statistical procedure designed to identify different subnetworks. As an example, we show the application of this tool in resting-state fMRI data obtained from the Human Connectome Project. We identify, among other variables, that the amount of sleep the days before the scan is a relevant variable that must be controlled. Finally, we discuss the potential bias in neuroimaging findings that is generated by some behavioural and brain structure variables. Our method can also be applied to other kind of networks such as protein interaction networks, gene networks or social networks.Fil: Fraiman Borrazás, Daniel Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Fraiman, Jacob Ricardo. Universidad de la República; Uruguay. Instituto Pasteur de Montevideo; Urugua

Variability in functional brain networks predicts expertise during action observation

Observing an action performed by another individual activates, in the observer, similar circuits as those involved in the actual execution of that action. This activation is modulated by prior experience; indeed, sustained training in a particular motor domain leads to structural and functional changes in critical brain areas. Here, we capitalized on a novel graph-theory approach to electroencephalographic data (Fraiman et al., 2016) to test whether variability in functional brain networks implicated in Tango observation can discriminate between groups differing in their level of expertise. We found that experts and beginners significantly differed in the functional organization of task-relevant networks. Specifically, networks in expert Tango dancers exhibited less variability and a more robust functional architecture. Notably, these expertise-dependent effects were captured within networks derived from electrophysiological brain activity recorded in a very short time window (2 s). In brief, variability in the organization of task-related networks seems to be a highly sensitive indicator of long-lasting training effects. This finding opens new methodological and theoretical windows to explore the impact of domain-specific expertise on brain plasticity, while highlighting variability as a fruitful measure in neuroimaging research.Fil: Amoruso, Lucía. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Neurociencia Cognitiva. Fundación Favaloro. Instituto de Neurociencia Cognitiva; Argentina. Università degli Studi di Udine; ItaliaFil: Ibáñez Barassi, Agustín Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Neurociencia Cognitiva. Fundación Favaloro. Instituto de Neurociencia Cognitiva; Argentina. Universidad Autónoma del Caribe; Colombia. Universidad Adolfo Ibañez; Chile. Australian Research Council; AustraliaFil: Fonseca, Bruno. Universidad de la República; UruguayFil: Gadea, Sebastián. Universidad de la República; UruguayFil: Sedeño, Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Neurociencia Cognitiva. Fundación Favaloro. Instituto de Neurociencia Cognitiva; ArgentinaFil: Sigman, Mariano. Universidad Torcuato di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: García, Adolfo Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Neurociencia Cognitiva. Fundación Favaloro. Instituto de Neurociencia Cognitiva; Argentina. Universidad Nacional de Cuyo. Facultad de Educación Elemental y Especial; ArgentinaFil: Fraiman, Jacob Ricardo. Universidad de la República; UruguayFil: Fraiman Borrazás, Daniel Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentin

Seeking relevant information from a statistical model

We herein introduce a general variable selection procedure, which can be applied to several parametric multivariate problems, including principal components and regression, among others. The aim is to allow the identification of a small subset of the original variables that can ‘better explain’ the model through nonparametric relationships. The method typically yields some noisy uninformative variables and some variables that are strongly related because of their general dependence and our aim is to help understand the underlying structures in a given data–set. The asymptotic behaviour of the proposed method is considered and some real and simulated data–sets are analysed as examples.Fil: Fraiman, Jacob Ricardo. Universidad de la República. Facultad de Ciencias; UruguayFil: Gimenez, Yanina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

On local times, density estimation and supervised classification from functional data

In this paper, we define a n-consistent nonparametric estimator for the marginal density function of an order one stationary process built up from a sample of i.i.d continuous time trajectories. Under mild conditions we obtain strong consistency, strong orders of convergence and derive the asymptotic distribution of the estimator. We extend some of the results to the non-stationary case. We propose a nonparametric classification rule based on local times (occupation measure) and include some simulations studies.Fil: Llop Orzan, Pamela Nerina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Fraiman, Jacob Ricardo. Universidad de la República; Urugua

A nonlinear aggregation type classifier

We introduce a nonlinear aggregation type classifier for functional data defined on a separable and complete metric space. The new rule is built up from a collection of M arbitrary training classifiers. If the classifiers are consistent, then so is the aggregation rule. Moreover, asymptotically the aggregation rule behaves as well as the best of the M classifiers. The results of a small simulation are reported both, for high dimensional and functional data, and a real data example is analyzed.Fil: Cholaquidis, Alejandro. Universidad de la República. Facultad de Ciencias; UruguayFil: Fraiman, Jacob Ricardo. Universidad de la República. Facultad de Ciencias; UruguayFil: Kalemkerian, Juan. Universidad de la República. Facultad de Ciencias; UruguayFil: Llop Orzan, Pamela Nerina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentin