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.

中文翻译：

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一种基于常微分方程的求解路径算法

Efron、Hastie、Johnstone 和 Tibshirani [(2004), 'Least Angle Regression (with Discussion)', The Annals of Statistics, 32, 409–499] 提出了最小角度回归 (LAR)，一种用于最小二乘法的解决路径算法回归。他们指出，对 LAR 稍作修改，即可获得 LASSO [Tibshirani, R. (1996), 'Regression Shrinkage and Selection Via the Lasso', Journal of the Royal Statistical Society, Series B, 58, 267–288] 求解路径. 然而，如何将这种解决方案路径算法扩展到最小二乘回归之外的模型在很大程度上是未知的。在这项工作中，我们通过显示相应的解路径是由常微分方程 (ODE) 系统的解分段给出的，提出了广义线性模型和拟似然模型的 LAR 的扩展。我们的贡献是双重的。第一的，我们提供了有关相应解决方案路径如何传播的理论理解。其次，我们提出了一种基于 ODE 的算法来获得整个解决方案路径。