Convex Modeling of Interactions with Strong Heredity.
Convex Modeling of Interactions with Strong Heredity.
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DOI：
10.1080/10618600.2015.1067217
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Simon N
中科院分区：
文献类型：
--
作者：
Haris A;Witten D;Simon N
我们考虑拟合一个回归模型的任务，该模型涉及一组潜在的大量协变量之间的相互作用，其中我们希望强制执行强遗传性。我们提出了FAMILY，这是一个非常通用的框架。我们的建议是几种现有方法的推广，例如VANISH，hierNet，所有对套索和仅使用主效应的套索。它可以配制成一个凸优化问题的解决方案，我们使用一个有效的交替方向方法的乘法器（ADMM）算法解决。该算法保证收敛到全局最优，可以很容易地专门为任何凸罚函数的利益，并允许一个简单的扩展到广义线性模型的设置。我们推导出一个无偏估计的自由度的家庭，并探讨其性能在模拟研究和HIV序列数据集。
We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a very general framework for this task. Our proposal is a generalization of several existing methods, such as VANISH, hierNet, the all-pairs lasso, and the lasso using only main effects. It can be formulated as the solution to a convex optimization problem, which we solve using an efficient alternating directions method of multipliers (ADMM) algorithm. This algorithm has guaranteed convergence to the global optimum, can be easily specialized to any convex penalty function of interest, and allows for a straightforward extension to the setting of generalized linear models. We derive an unbiased estimator of the degrees of freedom of FAMILY, and explore its performance in a simulation study and on an HIV sequence data set.