论文标题
改进的路径协调下降的功率惩罚
Improved Pathwise Coordinate Descent for Power Penalties
论文作者
论文摘要
路径坐标下降算法已用于计算整个套索的解决方案路径，并以巨大的成功来迅速迅速进行惩罚回归问题。他们通过解决构成解决方案路径的问题的问题来依次为一组调谐参数值组成解决方案路径的问题，而不是分别解决每个问题，它们会改善。但是，将路径的坐标级后裔算法扩展到更多的$ \ ell_q $惩罚的通用桥梁或电力家族具有挑战性。需要进行这些惩罚的更快计算解决方案路径算法，因为$ \ ell_q $惩罚回归问题可能是非convex，尤其是繁重的解决方案。在本文中，我们表明$ \ ell_q $惩罚回归问题的重新聚集化更适合路径坐标坐标下降算法。这使我们能够在实践中改善$ \ ell_q $惩罚回归问题的模式阈值函数的计算，并引入两个单独的路径算法。我们表明，路径算法要比相应的冷启动替代方案快，并且证明不同的路径算法可能更有可能达到更好的溶液。
Pathwise coordinate descent algorithms have been used to compute entire solution paths for lasso and other penalized regression problems quickly with great success. They improve upon cold start algorithms by solving the problems that make up the solution path sequentially for an ordered set of tuning parameter values, instead of solving each problem separately. However, extending pathwise coordinate descent algorithms to more the general bridge or power family of $\ell_q$ penalties is challenging. Faster algorithms for computing solution paths for these penalties are needed because $\ell_q$ penalized regression problems can be nonconvex and especially burdensome to solve. In this paper, we show that a reparameterization of $\ell_q$ penalized regression problems is more amenable to pathwise coordinate descent algorithms. This allows us to improve computation of the mode-thresholding function for $\ell_q$ penalized regression problems in practice and introduce two separate pathwise algorithms. We show that either pathwise algorithm is faster than the corresponding cold-start alternative, and demonstrate that different pathwise algorithms may be more likely to reach better solutions.
