Structure Learning via Hadamard Product of Correlation and Partial Correlation Matrices

Karina Ashurbekova 1, 2 Sophie Achard 2 Florence Forbes 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 GIPSA-VIBS - VIBS
GIPSA-DIS - Département Images et Signal
Abstract : Structure learning is an active topic nowadays indifferent application areas, i.e. genetics, neuroscience. Classical conditional independences or marginal independences may not be sufficient to express complex relationships. This paper is introducing a new structure learning procedure where an edge inthe graph corresponds to a non zero value of both correlation and partial correlation. Based on this new paradigm, we define an estimator and derive its theoretical properties. The asymptotic convergence of the proposed graph estimator and its rate are derived. Illustrations on a synthetic example and application to brain connectivity are displayed.
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Submitted on : Thursday, September 19, 2019 - 9:00:03 AM
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Karina Ashurbekova, Sophie Achard, Florence Forbes. Structure Learning via Hadamard Product of Correlation and Partial Correlation Matrices. EUSIPCO 2019 - 27th European Signal Processing Conference, Sep 2019, A Coruña, Spain. pp.1-5. ⟨hal-02290847⟩

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