一种通过新步长实现GAMLSS的平衡统计提升方法
A Balanced Statistical Boosting Approach for GAMLSS via New Step Lengths
AI总结：
针对GAMLSS分量式梯度提升中子模型不平衡问题，提出考虑拟合基学习器相对大小的自适应步长平衡提升方法，计算高效易推广，在多分布响应及多类数据任务中表现出竞争力。
摘要：
分量式梯度提升算法因其固有的变量选择和隐式正则化而广受欢迎，这对非常灵活的模型类别尤其有益。在通过分量式梯度提升算法估计位置、尺度和形状广义加性模型（GAMLSS）时，估计过程的一个重要部分是确定与不同分布参数对应的子模型的相对复杂度。现有方法要么存在调优过程计算成本高的问题，要么可能因负梯度大小的结构差异而产生偏差，一旦出现这种情况，就会导致不同子模型之间的不平衡。为了解决这个问题，已有研究提出用收缩最优步长代替仅限于高斯响应变量的非循环提升算法中典型的小固定步长。本文提出了一种新的自适应步长方法，该方法考虑了拟合基学习器的相对大小，以确保不同子模型之间的自然平衡。因此，这种新的平衡提升方法是收缩最优步长的一种计算高效且易于推广的替代方案。我们针对高斯分布、负二项分布以及威布尔分布的响应变量实现了平衡非循环提升算法，并通过模拟研究、对就诊次数建模的计数数据分析以及肿瘤学试验中的生存数据分析，证明了这种新的自适应步长方法具有竞争力的性能。
英文摘要：
Component-wise gradient boosting algorithms are popular for their intrinsic variable selection and implicit regularization, which can be especially beneficial for very flexible model classes. When estimating generalized additive models for location, scale and shape (GAMLSS) by means of a component-wise gradient boosting algorithm, an important part of the estimation procedure is to determine the relative complexity of the submodels corresponding to the different distribution parameters. Existing methods either suffer from a computationally expensive tuning procedure or can be biased by structural differences in the negative gradients' sizes, which, if encountered, lead to imbalances between the different submodels. Shrunk optimal step lengths have been suggested to replace the typical small fixed step lengths for a non-cyclical boosting algorithm limited to a Gaussian response variable in order to address this issue. In this article, we propose a new adaptive step length approach that accounts for the relative size of the fitted base-learners to ensure a natural balance between the different submodels. The new balanced boosting approach thus represents a computationally efficient and easily generalizable alternative to shrunk optimal step lengths. We implemented the balanced non-cyclical boosting algorithm for a Gaussian, a negative binomial as well as a Weibull distributed response variable and demonstrate the competitive performance of the new adaptive step length approach by means of a simulation study, in the analysis of count data modeling the number of doctor's visits as well as for survival data in an oncological trial.
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