This chapter fully introduces a scalable algorithm addressing the problem of parsimonious identification of nonlinear relationships. The algorithm is based on a variant of the least-angle selection (LARS) principle together with a batched random selection of slices of the processed data followed by a parsimonious selection step. The performance of the algorithm is compared to the performances of the state-of-the-art scikit-learnScikit-learn algorithms addressing the same problem, namely LarsCV, LassoCV and LassoLarsCV. The comparison results show promising comparative performances as well the ability of the proposed algorithm to handle extremely large number of features up to over 300,000 which remains intractable for the latter existing algorithms which struggle at around 30,000 features. The algorithm developed in this chapter is used in Chap. 11 in order to address the problem of partial observation targetsObservation target reconstruction.