  Sparse model selection by structural risk minimization leads to a set of a
few predictors, ideally a subset of the true predictors. This selection clearly
depends on the underlying loss function $\tilde L$. For linear regression with
square loss, the particular (functional) Gradient Boosting variant
$L_2-$Boosting excels for its computational efficiency even for very large
predictor sets, while still providing suitable estimation consistency. For more
general loss functions, functional gradients are not always easily accessible
or, like in the case of continuous ranking, need not even exist. To close this
gap, starting from column selection frequencies obtained from $L_2-$Boosting,
we introduce a loss-dependent ''column measure'' $\nu^{(\tilde L)}$ which
mathematically describes variable selection. The fact that certain variables
relevant for a particular loss $\tilde L$ never get selected by $L_2-$Boosting
is reflected by a respective singular part of $\nu^{(\tilde L)}$ w.r.t.
$\nu^{(L_2)}$. With this concept at hand, it amounts to a suitable change of
measure (accounting for singular parts) to make $L_2-$Boosting select variables
according to a different loss $\tilde L$. As a consequence, this opens the
bridge to applications of simulational techniques such as various resampling
techniques, or rejection sampling, to achieve this change of measure in an
algorithmic way.
