Wavelet-based graph inference using multiple testing

Sophie Achard; Pierre Borgnat; Irène Gannaz; Marine Roux

doi:10.1117/12.2529193

9 September 2019 Wavelet-based graph inference using multiple testing

Sophie Achard, Pierre Borgnat, Irène Gannaz, Marine Roux

Proceedings Volume 11138, Wavelets and Sparsity XVIII; 1113811 (2019) https://doi.org/10.1117/12.2529193
Event: SPIE Optical Engineering + Applications, 2019, San Diego, California, United States

Abstract

Graph-based representation enables to outline efficiently interactions between sensors and as such has encountered a growing interest. For example in neurosciences, the graph of interactions between brain regions has shed lights on evolution of diseases. In this paper, we describe a whole procedure which estimates the graph from multivariate time series. First correlations using wavelet decomposition of the signals are estimated. Bonferroni (1935)'s procedure on multiple correlation testing is then used. We prove theoretically that the Family Wise Error Rate (FWER) is asymptotically controlled for any graph structures. We implement our approach on smallworld graph structures, with signals possibly having long-memory properties. This structure is inspired by real data examples from resting-state functional magnetic resonance imaging. The control is confirmed graphically. Numerical simulations illustrate the behavior of the bias and the power of our proposed approach.

Citation Download Citation

Sophie Achard, Pierre Borgnat, Irène Gannaz, and Marine Roux "Wavelet-based graph inference using multiple testing", Proc. SPIE 11138, Wavelets and Sparsity XVIII, 1113811 (9 September 2019); https://doi.org/10.1117/12.2529193

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