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Parameter selection in high-dimensional models is typically finetuned in away that keeps the (relative) number of false positives under control. This isbecause otherwise the few true positives may be dominated by the many possiblefalse positives. This happens, for instance, when the selection follows from anaive optimisation of an information criterion, such as AIC or Mallows's Cp. Itcan be argued that the overestimation of the selection comes from theoptimisation process itself changing the statistics of the selected variables,in a way that the information criterion no longer reflects the true divergencebetween the selection and the data generating process. In lasso, theoverestimation can also be linked to the shrinkage estimator, which makes theselection too tolerant of false positive selections. For these reasons, thispaper works on refined information criteria, carefully balancing falsepositives and false negatives, for use with estimators without shrinkage. Inparticular, the paper develops corrected Mallows's Cp criteria for structuredselection in trees and graphical models.

Information criteria for structured parameter selection in high dimensional tree and graph models