Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

A partial graphical model with a structural prior on the direct links between predictors and responses

Abstract : This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between potentially high-dimensional predictors and multiple responses, since it is known that Gaussian graphical models enable to exhibit direct links only, whereas coefficients in linear regressions contain both direct and indirect relations (due \textit{e.g.} to strong correlations among the variables). A smooth penalty reflecting a generalized Gaussian Bayesian prior on the covariates is added, either enforcing patterns (like row structures) in the direct links or regulating the joint influence of predictors. We give a theoretical guarantee for our method, taking the form of an upper bound on the estimation error arising with high probability, provided that the model is suitably regularized. Empirical studies on synthetic data and a real dataset are conducted.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-02521004
Contributor : Frédéric Proïa <>
Submitted on : Friday, March 27, 2020 - 10:42:26 AM
Last modification on : Tuesday, May 25, 2021 - 7:45:08 AM

Links full text

Identifiers

  • HAL Id : hal-02521004, version 1
  • ARXIV : 2003.11869

Collections

Citation

Eunice Okome Obiang, Pascal Jézéquel, Frédéric Proïa. A partial graphical model with a structural prior on the direct links between predictors and responses. 2020. ⟨hal-02521004⟩

Share

Metrics

Record views

81