c-lasso -- a Python package for constrained sparse and robust regression and classification

arXiv2011.00898MaRDI QIDQ6352804

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Publication date: 2 November 2020

Abstract: We introduce c-lasso, a Python package that enables sparse and robust linear regression and classification with linear equality constraints. The underlying statistical forward model is assumed to be of the following form: [ y = X �eta + sigma epsilon qquad extrm{subject to} qquad C�eta=0 ] Here, $Xinmathbb{R}^{nimesd}$is a given design matrix and the vector $yinmathbb{R}^n$ is a continuous or binary response vector. The matrix $C$ is a general constraint matrix. The vector $$ contains the unknown coefficients and $sigma$ an unknown scale. Prominent use cases are (sparse) log-contrast regression with compositional data $X$, requiring the constraint $$ (Aitchion and Bacon-Shone 1984) and the Generalized Lasso which is a special case of the described problem (see, e.g, (James, Paulson, and Rusmevichientong 2020), Example 3). The c-lasso package provides estimators for inferring unknown coefficients and scale (i.e., perspective M-estimators (Combettes and M"uller 2020a)) of the form [ min_{�eta in mathbb{R}^d, sigma in mathbb{R}_{0}} fleft(X�eta - y,{sigma} ight) + lambda leftlVert �eta ight Vert_1 qquad extrm{subject to} qquad C�eta = 0 ] for several convex loss functions $f(cdot,cdot)$. This includes the constrained Lasso, the constrained scaled Lasso, and sparse Huber M-estimators with linear equality constraints.

Has companion code repository: https://github.com/Leo-Simpson/c-lasso

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