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

We introduce c-lasso, a Python package that enables sparse and robust linear regression classification with equality constraints. The underlying statistical forward model is assumed to be of the following form: \[ y = X \beta + \sigma \epsilon \qquad \textrm{subject to} C\beta=0 \] Here, $X \in \mathbb{R}^{n\times d}$is given design matrix vector $y \mathbb{R}^{n}$ continuous or binary response vector. $C$ general constraint matrix. $\beta \mathbb{R}^{d}$ contains unknown coefficients $\sigma$ an scale. Prominent use cases are (sparse) log-contrast compositional data $X$, requiring $1_d^T 0$ (Aitchion Bacon-Shone 1984) Generalized Lasso which special case described problem (see, e.g, (James, Paulson, Rusmevichientong 2020), Example 3). c-lasso provides estimators for inferring scale (i.e., perspective M-estimators (Combettes Muller 2020a)) form \min_{\beta \mathbb{R}^d, \mathbb{R}_{0}} f\left(X\beta - y,{\sigma} \right) \lambda \left\lVert \beta\right\rVert_1 C\beta 0 several convex loss functions $f(\cdot,\cdot)$. This includes constrained Lasso, scaled Huber