Using a multiplicative reparametrization, I show that a subclass of $L_q$
penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It
follows that the lasso and other norm-penalized regression estimates may be
obtained using a very simple and intuitive alternating ridge regression
algorithm. As compared to a similarly intuitive EM algorithm for $L_q$
optimization, the proposed algorithm avoids some numerical instability issues
and is also competitive in terms of speed. Furthermore, the proposed algorithm
can be extended to accommodate sparse high-dimensional scenarios, generalized
linear models, and can be used to create structured sparsity via penalties
derived from covariance models for the parameters. Such model-based penalties
may be useful for sparse estimation of spatially or temporally structured
parameters.

本文提出了多项式重新参数化方法，将 L_q 惩罚子集与 L_2 惩罚关联起来，提出了通过一种非常简单和直观的交替岭回归算法得出套索和其他规范化回归估计的方法，可避免一些数值不稳定性问题，同时在速度上也具有竞争力。此外，该算法可以扩展到适应稀疏高维情况、广义线性模型，并可用于通过参数协方差模型导出的惩罚项来创建结构稀疏。