A Nonparametric Graphical Model for Functional Data With Application to Brain Networks Based on fMRI

We introduce a nonparametric graphical model whose observations on vertices are functions. Many modern applications, such as electroencephalogram and functional magnetic resonance imaging (fMRI), produce data are of this type. The model is based on additive conditional independence (ACI), a statisti...

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Vydáno v:	Journal of the American Statistical Association Ročník 113; číslo 524; s. 1637 - 1655
Hlavní autoři:	Li, Bing, Solea, Eftychia
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Alexandria Taylor & Francis 02.10.2018 Taylor & Francis Group,LLC Taylor & Francis Ltd
Témata:	Additive conditional independence Additive correlation operator Additive precision operator Apexes Attention deficit hyperactivity disorder Brain Computer simulation Convergence data collection EEG electroencephalography equations fMRI Functional magnetic resonance imaging Functionals Gaussian graphical model Grammatical aspect heteroskedasticity Hilbert space Hyperactivity Independence Iterative methods Kernels Magnetic resonance imaging Mathematical models Matrices Nonparametric statistics Operators (mathematics) Optimization Patients Quantitative analysis Regression analysis Reproducing kernel Hilbert space Simulation Statistical methods Statistics Theory and Methods
ISSN:	0162-1459, 1537-274X, 1537-274X
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Shrnutí:	We introduce a nonparametric graphical model whose observations on vertices are functions. Many modern applications, such as electroencephalogram and functional magnetic resonance imaging (fMRI), produce data are of this type. The model is based on additive conditional independence (ACI), a statistical relation that captures the spirit of conditional independence without resorting to multi-dimensional kernels. The random functions are assumed to reside in a Hilbert space. No distributional assumption is imposed on the random functions: instead, their statistical relations are characterized nonparametrically by a second Hilbert space, which is a reproducing kernel Hilbert space whose kernel is determined by the inner product of the first Hilbert space. A precision operator is then constructed based on the second space, which characterizes ACI, and hence also the graph. The resulting estimator is relatively easy to compute, requiring no iterative optimization or inversion of large matrices. We establish the consistency and the convergence rate of the estimator. Through simulation studies we demonstrate that the estimator performs better than the functional Gaussian graphical model when the relations among vertices are nonlinear or heteroscedastic. The method is applied to an fMRI dataset to construct brain networks for patients with attention-deficit/hyperactivity disorder. Supplementary materials for this article are available online
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	0162-1459 1537-274X 1537-274X
DOI:	10.1080/01621459.2017.1356726