Stories about Fréchet Regression
2 related stories
Marginal Coordinate Test for Fr\'echet Regression with Random Objects
AI InsightThis paper introduces a marginal coordinate test for random-object regression in separable metric spaces, using a semi-supervised framework and a kernel conditional mean dependence U-statistic to test predictor informativeness without response residuals. Compared with prior residual-based tests, it relaxes assumptions and broadens applicability.Key TakeawayUnlike previous residual-based tests, this method avoids response residuals and works in general metric spaces.Why It MattersIt provides a more general hypothesis-testing tool for regression with complex structured responses, advancing statistical modeling on non-Euclidean data.Who's Affected- AI ResearchersGain a new theoretical tool to test conditional effects of predictors in random-object regression, extending statistical inference limits.
What's NextWatch for empirical performance on large semi-supervised datasets and theoretical adaptations to non-separable metric spaces or nonlinear relationships.Importance 70/100Test of partial effects for Frechet regression on Bures-Wasserstein manifolds
AI InsightA novel test for partial effects in Fréchet regression on the Bures-Wasserstein manifold is proposed. Compared to the previous lack of significance testing tools for responses on such manifolds, this method fills a gap in statistical inference. Validated by asymptotic theory and single-cell data application, this indicates that variable selection on complex manifold data now has a rigorously supported testing framework.Key TakeawayIntroduces significance testing for Bures-Wasserstein manifold regression.Why It MattersProvides an asymptotically valid and consistent theoretical method for variable selection on complex manifold data like covariance matrices, with practical value in single-cell gene co-expression analysis.What's NextFocus on the method's generalization to other non-Euclidean data structures (e.g., networks, trees) and its empirical power in high-dimensional, small-sample scenarios.Importance 65/100