c-lasso – a Python package for constrained sparse and robust regression and classification
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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 ∈ℝ^n× dis a given design matrix and the vector y ∈ℝ^n is a continuous or binary response vector. The matrix C is a general constraint matrix. The vector β∈ℝ^d 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_d^T 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 Müller 2020a)) of the form min_β∈ℝ^d, σ∈ℝ_0 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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