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Habilitation à diriger des recherches

Statistique des réseaux : inférence, comparaison et classification. Application à la connectivité cérébrale

Sophie Achard 1
1 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing
GIPSA-DIS - Département Images et Signal
Abstract : This manuscript presents my recent work on the statistical analysis of multivariate data structured in a network (or graph). A node in the network corresponds to a time series, and the edges or connections are linking two nodes. My research results in the statistical analysis of networks are divided in three parts : the inference, the comparison, and the classification of networks. Network inference consists in estimating the connections from the multivariate observations of a given system. The observed time series are often long memory and the usage of wavelets in order to compute the correlations introduces a bias in the estimation. We define the fractal connectivity in order to design estimators of corre- lations that are not affected by the presence of long memory. The network is then obtained by thresholding the correlations computed for pairs of nodes. The significant connections are extracted by using multiple testing procedures or maximum likelihood criterion opti- misations. Finally, I present applications of this research on the understanding of brain connectivity. My objective is to quantify differences between healthy volunteers and pa- tients. We are using functional magnetic resonance imaging (fMRI) to acquire noninvasive data on the brain functional process with a spatial resolution around 1 millimeter. The acquired data are multivariate time series where each time series corresponds to a spatial region of the brain. Networks for each subject are infered and then compared using topo- logical metrics like global efficiency or clustering, or using a score derived on a likelihood criterion. My investigations on new theoretical methods have been fertilised by their in- terdisciplinary context, at the intersection of signal and image processing, statistics and medical applications with genuine clinical outreach.
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Habilitation à diriger des recherches
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Sophie Achard. Statistique des réseaux : inférence, comparaison et classification. Application à la connectivité cérébrale. Méthodologie [stat.ME]. Univ. Grenoble Alpes, 2016. ⟨tel-02064855⟩

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