Algorithms for Fitting the Constrained Lasso
This work provides practical algorithm recommendations for statisticians and data scientists dealing with constrained regression problems, but it is incremental as it builds on existing lasso and optimization methods.
The paper tackles the problem of solving the constrained lasso, which extends the lasso to include linear constraints for incorporating prior information, by comparing algorithms like quadratic programming, ADMM, and a solution path method, showing that these methods can also estimate the generalized lasso with applications in various domains.
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior information into the model. In addition to quadratic programming, we employ the alternating direction method of multipliers (ADMM) and also derive an efficient solution path algorithm. Through both simulations and real data examples, we compare the different algorithms and provide practical recommendations in terms of efficiency and accuracy for various sizes of data. We also show that, for an arbitrary penalty matrix, the generalized lasso can be transformed to a constrained lasso, while the converse is not true. Thus, our methods can also be used for estimating a generalized lasso, which has wide-ranging applications. Code for implementing the algorithms is freely available in the Matlab toolbox SparseReg.