  Detecting influential features in non-linear and/or high-dimensional data is
a challenging and increasingly important task in machine learning. Variable
selection methods have thus been gaining much attention as well as
post-selection inference. Indeed, the selected features can be significantly
flawed when the selection procedure is not accounted for. We propose a
selective inference procedure using the so-called model-free "HSIC-Lasso" based
on the framework of truncated Gaussians combined with the polyhedral lemma. We
then develop an algorithm, which allows for low computational costs and
provides a selection of the regularisation parameter. The performance of our
method is illustrated by both artificial and real-world data based experiments,
which emphasise a tight control of the type-I error, even for small sample
sizes.
