A Fast Solution to the Lasso Problem with Equality Constraints
提出两阶段算法快速求解带等式约束的Lasso问题，适用于广义线性模型和Cox比例风险模型，在微生物组回归和骨髓瘤生存分析中展示了计算优势。
The equality-constrained lasso problem augments the standard lasso by imposing additional structure on regression coefficients. Despite the broad utilities of the equality-constrained lasso, existing algorithms are typically computationally inefficient and only applicable to linear and logistic models. In this paper, we devise a fast solution to the equality-constrained lasso problem with a two-stage algorithm: first obtaining candidate covariate subsets of increasing size from unconstrained lasso problems and then leveraging an efficient combined alternating direction method of multipliers/Newton-Raphson algorithm. Our proposed algorithm leads to substantial speedups in getting the solution path of the constrained lasso and can be easily adapted to generalized linear models and Cox proportional hazards models. We conduct extensive simulation studies to demonstrate the computational advantage of the proposed method over existing solvers. To further show the unique utility of our method, we consider two real-world data examples: a microbiome regression analysis and a myeloma survival analysis; neither example could be solved by naively fitting the constrained lasso problem on the full predictor set.