The SLOPE estimator has the particularity of having null components (sparsity) and components that are equal in absolute value (clustering). The number of clusters depends on the regularization parameter of the estimator. This parameter can be chosen as a trade-off between interpretability (with a small number of clusters) and accuracy (with a small mean squared error or a small prediction error). Finding such a compromise requires to compute the solution path, that is the function mapping the regularization parameter to the estimator. We provide in this article an algorithm to compute the solution path of SLOPE and show how it can be used to adjust the regularization parameter.

We provide a necessary and sufficient condition for the uniqueness of penalized least-squares estimators whose penalty term is given by a norm with a polytope unit ball, covering a wide range of methods including SLOPE, PACS, fused, clustered and classical LASSO as well as the related method of basis pursuit. We consider a strong type of uniqueness that is relevant for statistical problems. The uniqueness condition is geometric and involves how the row span of the design matrix intersects the faces of the dual norm unit ball, which for SLOPE is given by the signed permutahedron. Further considerations based this condition also allow to derive results on sparsity and clustering features. In particular, we define the notion of a SLOPE pattern to describe both sparsity and clustering properties of this method and also provide a geometric characterization of accessible SLOPE patterns.

MOTIVATION: In metabolomics, the detection of new biomarkers from Nuclear Magnetic Resonance (NMR) spectra is a promising approach. However, this analysis remains difficult due to the lack of a whole workflow that handles spectra pre-processing, automatic identification and quantification of metabolites and statistical analyses, in a reproducible way. RESULTS: We present ASICS, an R package that contains a complete workflow to analyse spectra from NMR experiments. It contains an automatic approach to identify and quantify metabolites in a complex mixture spectrum and uses the results of the quantification in untargeted and targeted statistical analyses. ASICS was shown to improve the precision of quantification in comparison to existing methods on two independent datasets. In addition, ASICS successfully recovered most metabolites that were found important to explain a two level condition describing the samples by a manual and expert analysis based on bucketing. It also found new relevant metabolites involved in metabolic pathways related to risk factors associated with the condition. AVAILABILITY AND IMPLEMENTATION: ASICS is distributed as an R package, available on Bioconductor. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.