quality:corruption
Computing lasso solutions

The loss function of the lasso is not differentiable, but a wide variety of techniques from convex analysis and optimization theory have been developed to compute the solutions path of the lasso. These include coordinate descent, subgradient methods, least-angle regression (LARS), and proximal gradient methods. Subgradient methods are the natural generalization of traditional methods such as gradient descent and stochastic gradient descent to the case in which the objective function is not differentiable at all points. LARS is a method that is closely tied to lasso models, and in many cases allows them to be fit efficiently, though it may not perform well in all circumstances. LARS generates complete solution paths. Proximal methods have become popular because of their flexibility and performance and are an area of active research. The choice of method will depend on the particular lasso variant, the data and the available resources. However, proximal methods generally perform well.