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C-3PO
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Covariate Importance Testing for Compositional Data via Partial Conjunction
A framework for covariate importance testing and controlled variable selection when the covariates are compositional - their values sum to a fixed constant. Because that sum constraint makes each covariate a deterministic function of the others, every covariate is automatically conditionally independent of the response given the rest, so standard importance tests and variable-selection methods (which all reduce to conditional-independence testing) are powerless. The paper defines a unique, well-posed notion of a relevant compositional covariate, then constructs valid hypothesis tests and controlled selection procedures through a novel connection between bivariate conditional-independence testing and partial-conjunction hypothesis testing, with theoretical validity guarantees and demonstrated power.