通过双变量假设的部分合取进行成分协变量重要性检验
Compositional Covariate Importance Testing via Partial Conjunction of Bivariate Hypotheses
AI总结：
本文针对成分协变量在回归中因总和约束导致传统条件独立性检验失效的问题，提出将相关协变量概念转化到成分数据设定中，并基于双变量条件独立性检验与部分合取假设检验开发了新的重要性检验和变量选择方法，同时给出理论保证和实验验证。
摘要：
成分数据（即由总和为常数的随机变量组成的数据）出现在许多应用中，包括微生物组研究、化学生态学、政治科学和实验设计。然而，当成分数据在回归中作为协变量时，总和约束使得每个协变量在给定其他协变量的条件下自动与响应变量条件独立，因为每个协变量都是其他协变量的确定性函数。由于几乎所有协变量重要性检验和变量选择方法（包括参数化方法）的核心都是检验条件独立性，它们在具有成分协变量的回归问题上完全无能为力。事实上，成分性使得相关协变量这一概念本身就存在歧义。为了解决这个问题，我们确定了一种自然的方式，将相关协变量的典型概念转化到具有成分协变量的设定中，并证明该概念是直观的、定义良好的且唯一的。然后，我们通过与双变量条件独立性检验和部分合取假设检验的新颖联系，开发了相应的假设检验和受控变量选择程序。最后，我们提供了方法有效性的理论保证，并通过数值实验证明我们的方法不仅有效，而且在各种数据生成场景下都具有较高的检验功效。
英文摘要：
Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve as covariates in a regression, the sum constraint renders every covariate automatically conditionally independent of the response given the other covariates, since each covariate is a deterministic function of the others. Since essentially all covariate importance tests and variable selection methods, including parametric ones, are at their core testing conditional independence, they are all completely powerless on regression problems with compositional covariates. In fact, compositionality causes ambiguity in the very notion of relevant covariates. To address this problem, we identify a natural way to translate the typical notion of relevant covariates to the setting with compositional covariates and establish that it is intuitive, well-defined, and unique. We then develop corresponding hypothesis tests and controlled variable selection procedures via a novel connection with \emph{bivariate} conditional independence testing and partial conjunction hypothesis testing. Finally, we provide theoretical guarantees of the validity of our methods, and through numerical experiments demonstrate that our methods are not only valid but also powerful across a range of data-generating scenarios.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
