Generalized Information Criteria for Model Selection Consistency of M-Estimators in High Dimensions: A Unified Framework


  • Gabriel Jardim Pereira Pinto


11/04/2019 - 13:00


Auditório 537


Regularized M-estimators have been widely used in science, due to their ability to fit a simpler, lower-dimensional model in higher-dimensional scenarios. Usually, the low-dimensional structure is assumed to be part of the underlying data-generating processes, affecting the unknown parameters and their estimation in various manners. Some of the recent efforts on the subject have focused on the creation of an unified framework, and the establishment of sufficient conditions for consistency and model selection consistency. By tapping into the literature on Information Criteria (IC), we use that same general setting to derive sufficient conditions for the Model Selection consistency of a GIC type selector and the path-consistency of regularized M-estimators. Here, path-consistency means that the probability the solution path contains the true model converges to 1, allowing the practical use of IC for Model Selection in high-dimensional scenarios. We then prove those conditions hold for some examples, such as the Lasso and the Group Lasso, with various loss functions.

*Texto enviado pelo aluno. 

Membros da banca: 

  • Eduardo Fonseca Mendes (orientador) – FGV EMAp
  • Marcelo Cunha Medeiros - PUC
  • Flávio Ziegelmann - UFRGS