Séminaire Datashape
Generalized Information Criteria for Structured Sparse Models
nov. 2021
Intervenant : Eduardo Mendes
Institution : Fundação Getúlio Vargas, Rio de Janeiro
Heure : 15h45 - 16h45
Lieu : 3L15

Regularized M-estimators are widely used due to their ability of recovering a low-dimensional model in high-dimensional scenarios. Some recent efforts on this subject focused on creating a unified framework for establishing oracle bounds and deriving conditions for support recovery. Under this same framework, we propose a new Generalized Information Criteria that takes into consideration the sparsity pattern one wishes to recover. We obtain non-asymptotic model selection bounds and sufficient conditions for model selection consistency of the GIC. Furthermore, we show that one may use the GIC for selecting the regularization parameter in a way that the sequence of model subspaces contains the true model with probability converging to one. This allows practical use of the GIC for model selection in high-dimensional scenarios. We illustrate those conditions on examples including group LASSO generalized linear regression and low rank matrix regression.

It is joint work with a former student (Gabriel Pinto PhD Student @ Northwestern University).

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