Papers › c-lasso -- a Python package for constrained sparse and robust regression and classification
c-lasso -- a Python package for constrained sparse and robust regression and classification
Léo Simpson, Patrick L. Combettes, Christian L. Müller
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 β+ σϵ subject to Cβ=0 Here, $X \in \mathbb{R}^{n\times d}$is a given design matrix and the vector y ∈ℝⁿ is a continuous or binary response vector. The matrix C is a general constraint matrix. The vector β∈ℝᵈ contains the unknown coefficients and σ an unknown scale. Prominent use cases are (sparse) log-contrast regression with compositional data X, requiring the constraint 1_dᵀ β= 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_(β∈ℝᵈ, σ∈ℝ₀) f(Xβ- y,σ ) + λ‖β‖₁ subject to Cβ= 0 for several convex loss functions f(·,·). This includes the constrained Lasso, the constrained scaled Lasso, and sparse Huber M-estimators with linear equality constraints.
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