Simulated Data for Linear Regression with Structured and Sparse Penalties

Tommy Lofstedt , Vincent Guillemot , Vincent Frouin (1) , Edouard Duchesnay (2, 3) , Fouad Hadj-Selem

1 NEUROSPIN - Service NEUROSPIN
2 LNAO - Laboratoire de Neuroimagerie Assistée par Ordinateur
3 IFR 49 - IFR de Neuroimagerie Fonctionnelle

The integration of structure in Machine Learning methods is a very active field in Bioinformatics. Methods recently developed claim that they allow at the same time to link the computed model to the graphical structure of the data set and to select a handful of important features in the analysis. We nevertheless lack simulated data for which we can separate the three properties that the method claim achieving: (i) the sparsity of the solution, i.e. the fact the the model is based on a few features of the data; (ii) the structure of the model; (iii) the relation between the structure of the model and the graphical model behind the generation of the data. We propose a framework to simulate data for linear regression while controlling their signal-to-noise ratio, their internal correlation structure and knowing exactly the optimization problem they are a solution of. Plus, we do not make any strong statistical assumption on the distribution of the data set.

Mots clés: Data simulation; linear regression; complex penalties

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Apprentissage [cs.LG]

Tommy Lofstedt, Vincent Guillemot, Vincent Frouin, Edouard Duchesnay, Fouad Hadj-Selem. Simulated Data for Linear Regression with Structured and Sparse Penalties. 2013. ⟨cea-00914960v1⟩