Graph-Adaptive Horseshoe for Compositional Regression
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用于成分回归的图自适应马蹄先验
- 研究问题
- 成分型预测变量受总和约束且相互依赖，如何同时进行变量选择，并学习与结果相关而非预先固定的正则化关系图？
- 方法与思路
- 作者提出贝叶斯GRACE框架，通过线性重参数化满足成分约束，结合结构化马蹄先验、边权先验与Gibbs抽样学习图结构。
- 材料陈述的贡献
- 摘要称，该框架提供稀疏估计和图结构后验不确定性，在模拟中表现出有竞争力的预测精度，并改善图恢复表现。
- 阅读关注点
- 应核对成分约束的参数化、图与回归系数的可辨识性、先验敏感性、抽样收敛，以及图误设下比较实验的设计。
- 阅读边界
- 这是arXiv预印本，同行评审或期刊接收未获核验。摘要未提供性能数值；微生物应用中的结果关联与所学图不能直接解释为因果关系。
原文摘要
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.