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Marginal Coordinate Test for Fréchet Regression with Random Objects

arXiv · AI, language, vision and robotics · article · Aug 31, 2026 · UTC

We develop a marginal coordinate test for regression with Euclidean predictors and a random-object response in a separable metric space. The goal is to test whether a predictor provides additional information about the response conditional on the remaining predictors. In a semi-supervised design, an unlabeled sample is used to estimate predictor conditional means, while an independent labeled sample is reserved for inference. The resulting residuals are combined with a product-space kernel to form a kernel conditional mean dependence (KCMD) U-statistic without requiring a response residual. Th

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