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Eftychia SOLEA (CREST-ENSAI) “High-dimensional Nonparametric Functional Graphical Models via the Functional Additive Partial Correlation Operator ”
Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 30th of January 2023
Place: Room 3001
Eftychia SOLEA (CREST-ENSAI) – “High-dimensional Nonparametric Functional Graphical Models via the Functional Additive Partial Correlation Operator ”
This article develops a novel approach for estimating a high-dimensional and nonparametric graphical model for functional data. Our approach is built on a new linear operator, the functional additive partial correlation operator, which extends the partial correlation matrix to both the nonparametric and functional settings. We show that its nonzero elements can be used to characterize the graph, and we employ sparse regression techniques for graph estimation. Moreover, the method does not rely on any distributional assumptions and does not require the computation of multi-dimensional kernels, thus avoiding the curse of dimensionality. We establish both estimation consistency and graph selection consistency of the proposed estimator, while allowing the number of nodes to grow with the increasing sample size. Through simulation studies, we demonstrate that our method performs better than existing methods in cases where the Gaussian or Gaussian copula assumption does not hold. We also demonstrate the performance of the proposed method by a study of an electroencephalography data set to construct a brain network.
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)