A weight-relaxed model averaging approach for high-dimensional generalized linear models
高维广义线性模型的权重放松模型平均AI 解读 ↓
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高维广义线性模型的权重放松模型平均
- 研究问题
- 允许预测变量数量随样本量增长时，放松模型总权重约束的平均方法如何从线性模型推广至可能设定错误的广义线性模型？
- 方法与思路
- 作者先建立误设模型中伪真回归参数的存在性，再分析留一交叉验证选权，并通过偏差与方差的分解和界定处理证明困难。
- 材料陈述的贡献
- 摘要称证明伪真参数存在，并给出交叉验证权重选择达到渐近最优的条件；模拟用于展示相对多种正则化及模型平均方法的表现。
- 阅读关注点
- 阅读时应核对误设模型中的伪真目标、权重可行域、维度增长与最优性条件，以及模拟比较的损失和数据生成设定。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；最优性条件、评价损失与模拟数值未给出，不能据此认定方法在所有高维任务中更好。
原文摘要
Model averaging has long been proposed as a powerful alternative to model selection in regression analysis. However, how well it performs in high-dimensional regression is still poorly understood. Recently, Ando and Li [J. Amer. Statist. Assoc. 109 (2014) 254–265] introduced a new method of model averaging that allows the number of predictors to increase as the sample size increases. One notable feature of Ando and Li’s method is the relaxation on the total model weights so that weak signals can be efficiently combined from high-dimensional linear models. It is natural to ask if Ando and Li’s method and results can be extended to nonlinear models. Because all candidate models should be treated as working models, the existence of a theoretical target of the quasi maximum likelihood estimator under model misspecification needs to be established first. In this paper, we consider generalized linear models as our candidate models. We establish a general result to show the existence of pseudo-true regression parameters under model misspecification. We derive proper conditions for the leave-one-out cross-validation weight selection to achieve asymptotic optimality. Technically, the pseudo true target parameters between working models are not linearly linked. To overcome the encountered difficulties, we employ a novel strategy of decomposing and bounding the bias and variance terms in our proof. We conduct simulations to illustrate the merits of our model averaging procedure over several existing methods, including the lasso and group lasso methods, the Akaike and Bayesian information criterion model-averaging methods and some other state-of-the-art regularization methods.