标题： 树引导的高维回归特征聚合的直接方法 显示英文标题

标题： A direct approach to tree-guided feature aggregation for high-dimensional regression

摘要： 在高维线性模型中，通常利用稀疏性来减少变异性并实现简约性。等稀疏性，即假设预测变量可以聚合成具有相同效应的组，是一种替代的简约结构，在某些应用中可能更为合适。先前的研究已经明确展示了在存在“罕见特征”时利用等稀疏性的优势（Yan和Bien 2021）。在本工作中，我们提出了一种新的树引导正则化方案，用于同时估计和特征聚合。与现有方法不同，我们的估计器避免了合成过参数化及其有害影响。尽管我们的惩罚应用于层次重叠的组，但我们证明其近端算子可以通过一次传递、非迭代算法求解。我们开发了新技术，在最小二乘和二项偏差损失下研究了这种半范数诱导正则化器的有限样本误差界。理论上，与现有方法相比，所提出的方法根据真实的等稀疏结构提供更快或相等的速率。广泛的模拟研究验证了这些发现。最后，我们通过一个微生物组数据集的应用说明了所提方法的有用性，在该应用中我们对聚合特征的影响进行了选择后推断。 显示英文摘要

摘要： In high-dimensional linear models, sparsity is often exploited to reduce variability and achieve parsimony. Equi-sparsity, where one assumes that predictors can be aggregated into groups sharing the same effects, is an alternative parsimonious structure that can be more suitable in certain applications. Previous work has clearly demonstrated the benefits of exploiting equi-sparsity in the presence of ``rare features'' (Yan and Bien 2021). In this work, we propose a new tree-guided regularization scheme for simultaneous estimation and feature aggregation. Unlike existing methods, our estimator avoids synthetic overparameterization and its detrimental effects. Even though our penalty is applied to hierarchically overlapped groups, we show that its proximal operator can be solved with a one-pass, non-iterative algorithm. Novel techniques are developed to study the finite-sample error bound of this seminorm-induced regularizer under least squares and binomial deviance losses. Theoretically, compared to existing methods, the proposed method offers a faster or equivalent rate depending on the true equi-sparisty structure. Extensive simulation studies verify these findings. Finally, we illustrate the usefulness of the proposed method with an application to a microbiome dataset, where we conduct post-selection inference on the aggregated features' effects.