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The direpack package establishes a set of modern statistical dimensionality reduction techniques into the Python universe as a single, consistent package. Several of the methods included are only available as open source through direpack, whereas the package also offers competitive Python implementations of methods previously only available in other programming languages. In its present version, the package is structured in three subpackages for different approaches to dimensionality reduction: projection pursuit, sufficient dimension reduction and robust M estimators. As a corollary, the package also provides access to regularized regression estimators based on these reduced dimension spaces, as well as a set of classical and robust preprocessing utilities, including very recent developments such as generalized spatial signs. Finally, direpack has been written to be consistent with the scikit-learn API, such that the estimators can flawlessly be included into (statistical and/or machine) learning pipelines in that framework.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which rely on minimal to no model assumptions. These are defined according to an optimization criterion that maximizes a nonparametric measure of association. The original estimators are nonsparse, which means that all variables contribute to the model. However, in many practical applications, an SDR technique may be called for that is sparse and as such, intrinsically performs sufficient variable selection (SVS). This paper examines how such a sparse SDR estimator can be constructed. Three variants are investigated, depending on different measures of association: distance covariance, martingale difference divergence and ball covariance. A simulation study shows that each of these estimators can achieve correct variable selection in highly nonlinear contexts, yet are sensitive to outliers and computationally intensive. The study sheds light on the subtle differences between the methods. Two examples illustrate how these new estimators can be applied in practice, with a slight preference for the option based on martingale difference divergence in the bioinformatics example.