Desparsifying -norm penalized estimators and corresponding theory can also be applied to models with convex loss functions such as generalized linear models.
Consider the following vectors of covariables and univariate responses for
we have a loss function
which is assumed to be strictly convex function in
The -norm regularized estimator is
Similarly, the Lasso for node wise regression with matrix input is defined as follows:
Denote by a matrix which we want to approximately invert using nodewise lasso.
The de-sparsified -norm regularized estimator is as follows:
where denotes the th row of without the diagonal element , and is the sub matrix without the th row and th column.