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

2020/11/02 by Simpson, Léo, Combettes, Patrick L., Müller, Christian L.
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Mathematical Software (cs.MS) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2011.00898

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 β+ σε \textrmsubject to Cβ=0 Here, X ∈ ℝ^{n× 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∈ 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∈ ℝ₀ f(Xβ- y,σ ) + λ‖ β‖₁ \textrmsubject 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.

Related

• The degrees of freedom of the Lasso for general design matrix
• Thresholded Lasso for high dimensional variable selection
• Thresholded Lasso for high dimensional variable selection and statistical estimation
• Robust Lasso with missing and grossly corrupted observations
• The Smooth-Lasso and other ℓ₁+ℓ₂-penalized methods