Robust structure learning using multivariate T-distributions

Karina Ashurbekova 1, 2 Sophie Achard 3 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-CICS - CICS
GIPSA-DIS - Département Images et Signal
3 GIPSA-VIBS - VIBS
GIPSA-DIS - Département Images et Signal
Abstract : We address the issue of robust graph structure learning in continuous settings. We focus on sparse precision matrix estimation for its tractability and ability to reveal some measure of dependence between variables. For this purpose, we propose to extract good features from existing methods, namely tlasso and CLIME procedures. The former is based on the observation that standard Gaussian modelling results in procedures that are too sensitive to outliers and proposes the use of t-distributions as an alternative.
The latter is an alternative to the popular Lasso optimization principle which can handle some of its limitations. We then combine these ideas into a new procedure referred to as tCLIME that can be seen as a modified tlassoalgorithm. Numerical performance is investigated using simulated data and reveals that tCLIME performs favorably comparedto the other standard methods.
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Conference papers
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Submitted on : Monday, December 3, 2018 - 10:44:30 AM
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Karina Ashurbekova, Sophie Achard, Florence Forbes. Robust structure learning using multivariate T-distributions. 50e Journées de la Statistique (JdS'2018), May 2018, Saclay, France. pp.1-6. 〈hal-01941643〉

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