The main goal of supervised data analytics is to model a target phenomenon given a limited amount of samples, each represented by an arbitrarily large number of variables. Especially when the number of variables is much larger than the number of available samples, variable selection is a key step as it allows to identify a possibly reduced subset of relevant variables describing the observed phenomenon. Obtaining interpretable and reliable results, in this highly indeterminate scenario, is often a non-trivial task. In this work we present PALLADIO, a framework designed for HPC cluster architectures, that is able to provide robust variable selection in high-dimensional problems. PALLADIO is developed in Python and it integrates CUDA kernels to decrease the computational time needed for several independent element-wise operations. The scalability of the proposed framework is assessed on synthetic data of different sizes, which represent realistic scenarios.