|
Abstract:
|
We compare alternative computing strategies for solving the constrained lasso problem proposed by James et al. (2013). As its name suggests, the constrained lasso extends the widely-used lasso (Tibshirani, 1996) 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 the generalized lasso, which has wide-ranging applications (Tibshirani and Taylor, 2011). Code for implementing the algorithms will be freely available in a MATLAB toolbox.
|
