  Simultaneously performing variable selection and inference in
high-dimensional regression models is an open challenge in statistics and
machine learning. The increasing availability of vast amounts of variables
requires the adoption of specific statistical procedures to accurately select
the most important predictors in a high-dimensional space, while controlling
the False Discovery Rate (FDR) arising from the underlying multiple hypothesis
testing. In this paper we propose the joint adoption of the Mirror Statistic
approach to FDR control, coupled with outcome randomisation to maximise the
statistical power of the variable selection procedure. Through extensive
simulations we show how our proposed strategy allows to combine the benefits of
the two techniques. The Mirror Statistic is a flexible method to control FDR,
which only requires mild model assumptions, but requires two sets of
independent regression coefficient estimates, usually obtained after splitting
the original dataset. Outcome randomisation is an alternative to Data
Splitting, that allows to generate two independent outcomes, which can then be
used to estimate the coefficients that go into the construction of the Mirror
Statistic. The combination of these two approaches provides increased testing
power in a number of scenarios, such as highly correlated covariates and high
percentages of active variables. Moreover, it is scalable to very
high-dimensional problems, since the algorithm has a low memory footprint and
only requires a single run on the full dataset, as opposed to iterative
alternatives such as Multiple Data Splitting.
