用于成分回归的图自适应马蹄形先验
Graph-Adaptive Horseshoe for Compositional Regression
AI总结：
本研究提出用于成分回归的GRACE贝叶斯框架，自适应学习结果驱动的收缩图，在模拟和口腔微生物组数据应用中表现出更优性能，证实自适应图对成分回归的重要性。
AI中文摘要：
微生物组丰度等成分型预测因子因单位和约束及固有依赖关系，给变量选择带来独特挑战。现有方法常依赖从系统发育或生态距离推导的固定关联图，可能无法反映与结果相关的关系。我们提出GRACE（用于成分回归的图自适应马蹄形先验，GRaph-Adaptive horseshoe for Compositional rEgression），这是一个完全贝叶斯框架，可强制执行成分约束、执行变量选择并自适应学习结果驱动的收缩图。GRACE通过回归系数的新型线性重参数化实现成分性，而结构化马蹄形先验会诱导稀疏性并沿学习到的图平滑系数。图学习通过对边权重施加缩放beta2先验完成，提供结果特定的自适应和后验不确定性量化。我们开发了结合椭圆切片采样的高效吉布斯采样器，以确保高维场景下的可扩展性。通过广泛模拟，GRACE与现有方法相比表现出有竞争力的预测准确性和改进的图恢复能力，尤其在图误设情况下优势明显。将其应用于ORIGINS研究的口腔微生物组数据，可识别与胰岛素抵抗相关的分类群，并生成总结这些分类群与结果关系的结果驱动图，该结构与系统发育或共现网络显著不同。这些发现表明，对正则化有用的固定预测因子图可能无法忠实地代表与结果相关的特征关系，凸显了成分回归中需要自适应、结果导向的方法。
英文摘要：
Compositional predictors, such as microbiome abundances, pose unique challenges in variable selection due to their unit-sum constraint and inherent dependencies. Existing approaches often rely on fixed association graphs derived from phylogenetic or ecological distances, which may not reflect outcome-relevant relationships. We propose GRACE (GRaph-Adaptive horseshoe for Compositional rEgression), a fully Bayesian framework that enforces compositional constraints, performs variable selection, and adaptively learns an outcome-driven shrinkage graph. GRACE achieves compositionality through a novel linear reparameterization of regression coefficients, while a structured horseshoe prior induces sparsity and smooths coefficients along the learned graph. Graph learning is accomplished via scaled beta2 priors on edge weights, providing both outcome-specific adaptation and posterior uncertainty quantification. We develop an efficient Gibbs sampler incorporating elliptical slice sampling to ensure scalability in high dimensions. Through extensive simulations, GRACE demonstrates competitive predictive accuracy and improved graph recovery compared with existing methods, particularly under graph misspecification. Application to oral microbiome data from the ORIGINS study identifies taxa associated with insulin resistance and yields an outcome-driven graph summarizing how those taxa relate to the outcome, a structure that differs substantially from phylogenetic or co-occurrence networks. These findings highlight that fixed predictor graphs useful for regularization may not faithfully represent outcome-relevant feature relationships, underscoring the need for adaptive, outcome-informed approaches in compositional regression.
