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
2 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing

Structure learning is an active topic nowadays in different 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 in the 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.

Mots clés: soft-thresholding; Hadamard product; marginal independence; structure learning; brain connectivity; conditional independence

Domaines: Méthodologie [stat.ME]; Applications [stat.AP]

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 Coruna, Spain. pp.1-5, ⟨10.23919/EUSIPCO.2019.8902948⟩. ⟨hal-02290847⟩