Sparse model selection

On choosing the right model and regularisation parameter in sparse regression, which turn out to be very nearly the same, and closely coupled to doing the regression. There are some wrinkles.


🏗 Explain my laborious reasoning that generalised Akaike information criteria don’t seem work when the penalty term is not continuous (e.g. \(L_1\) ), and the issues that therefore arise in model selection for such cases. Present alternatives for choosing the optimal regularisation coefficient, especially outside cross-validation, especially computationally tractable ones. Maybe even classical statistical hypothesis testing. Methods based on statistical learning theory or concentration inequalities win gratitude.


The new hotness sweeping the world is FOCI, a sparse model selection procedure (Azadkia and Chatterjee 2019) based on Chatterjee’s ξ statistic as an independence test test. (Chatterjee 2020). Looks interesting.

Stability selection


Relaxed Lasso


Dantzig Selector




Degrees-of-freedom penalties

See degrees of freedom.

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