  The Lasso regression is a popular regularization method for feature selection
in statistics. Prior to computing the Lasso estimator in both linear and
generalized linear models, it is common to conduct a preliminary rescaling of
the feature matrix to ensure that all the features are standardized. Without
this standardization, it is argued, the Lasso estimate will unfortunately
depend on the units used to measure the features. We propose a new type of
iterative rescaling of the features in the context of generalized linear
models. Whilst existing Lasso algorithms perform a single scaling as a
preprocessing step, the proposed rescaling is applied iteratively throughout
the Lasso computation until convergence. We provide numerical examples, with
both real and simulated data, illustrating that the proposed iterative
rescaling can significantly improve the statistical performance of the Lasso
estimator without incurring any significant additional computational cost.
