Graph inference by multiple testing with application to Neuroimaging

Abstract : This thesis is motivated by the analysis of the functional magnetic resonance imaging (fMRI). The need for methods to build such structures from fMRI data gives rise to exciting new challenges for mathematics. In this regards, the brain connectivity networks are modelized by a graph and we study some procedures that allow us to infer this graph.More precisely, we investigate the problem of the inference of the structure of an undirected graphical model by a multiple testing procedure. The structure induced by both the correlation and the partial correlation are considered. The statistical tests based on the latter are known to be highly dependent and we assume that they have an asymptotic Gaussian distribution. Within this framework, we study some multiple testing procedures that allow a control of false edges included in the inferred graph.First, we theoretically examine the False Discovery Rate (FDR) control of Benjamini and Hochberg’s procedure in Gaussian setting for non necessary positive dependent statistical tests. Then, we explore both the FDR and the Family Wise Error Rate (FWER) control in asymptotic Gaussian setting. We present some multiple testing procedures, well-suited for correlation (resp. partial correlation) tests, which provide an asymptotic control of the FWER. Furthermore, some first theoretical results regarding asymptotic FDR control are established.Second, the properties of the multiple testing procedures that asymptotically control the FWER are illustrated on a simulation study, for statistical tests based on correlation. We finally conclude with the extraction of cerebral connectivity networks on real data set.
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Marine Roux. Graph inference by multiple testing with application to Neuroimaging. Signal and Image processing. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAT058⟩. ⟨tel-01971574⟩

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