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

TL;DR

c-lasso is a Python package that offers constrained sparse and robust regression and classification methods, accommodating linear equality constraints, with applications in compositional data and generalized Lasso.

Contribution

The paper introduces c-lasso, a new Python package implementing constrained sparse and robust regression estimators with various convex loss functions.

Findings

Provides estimators for unknown coefficients and scale.

Supports multiple convex loss functions including Huber and Lasso.

Enables regression with linear equality constraints.

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: \[ y = X \beta + \sigma \epsilon \qquad \textrm{subject to} \qquad C\beta=0 \] Here, $X \in \mathbb{R}^{n\times d}$is a given design matrix and the vector $y \in \mathbb{R}^{n}$ is a continuous or binary response vector. The matrix $C$ is a general constraint matrix. The vector $\beta \in \mathbb{R}^{d}$ contains the unknown coefficients and $\sigma$ an unknown scale. Prominent use cases are (sparse) log-contrast regression with compositional data $X$, requiring the constraint $1_d^T \beta = 0$ (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 \[ \min_{\beta \in \mathbb{R}^d, \sigma \in \mathbb{R}_{0}} f\left(X\beta - y,{\sigma} \right) + \lambda \left\lVert \beta\right\rVert_1 \qquad \textrm{subject to} \qquad C\beta = 0 \] 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.