An ordinary differential equation-based solution path algorithm
An ordinary differential equation-based solution path algorithm
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DOI：
10.1080/10485252.2010.490584
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发表时间：
2011-01-01
影响因子：
1.2
通讯作者：
Wu, Yichao
中科院分区：
文献类型：
--
作者：
Wu, Yichao
Efron，Hastie，Johnstone和Tibshiani[(2004)，《最小角度回归(带讨论)》，The Annals of Statistics，32,409-499]提出了最小角度回归(LAR)，一种求解最小二乘回归的路径算法。他们指出，对LAR的轻微修改给出了套索[Tibishani，R.(1996)]的解决方案，《通过套索进行回归收缩和选择》，《皇家统计学会杂志》，B系列，58,267-288]。然而，如何将这种求解路径算法扩展到最小二乘回归以外的模型，在很大程度上是未知的。在这项工作中，我们提出了广义线性模型和拟似然模型的LAR的推广，证明了相应的解路径是由常微分方程组的解分段给出的。我们的贡献是双重的。首先，我们从理论上理解了相应的解路径是如何传播的。其次，我们提出了一种基于ODE的算法来获得整个解路径。
Efron, Hastie, Johnstone, and Tibshirani [(2004), 'Least Angle Regression (with discussions)', The Annals of Statistics, 32, 409-499] proposed least angle regression (LAR), a solution path algorithm for the least squares regression. They pointed out that a slight modification of the LAR gives the LASSO [Tibshirani, R. (1996), 'Regression Shrinkage and Selection Via the Lasso', Journal of the Royal Statistical Society, Series B, 58, 267-288] solution path. However, it is largely unknown how to extend this solution path algorithm to models beyond the least squares regression. In this work, we propose an extension of the LAR for generalised linear models and the quasi-likelihood model by showing that the corresponding solution path is piecewise given by solutions of ordinary differential equation (ODE) systems. Our contribution is twofold. First, we provide a theoretical understanding on how the corresponding solution path propagates. Second, we propose an ODE-based algorithm to obtain the whole solution path.