aiqbench analysis
This paper introduces a rigorous statistical test for assessing partial effects in Fréchet regression, specifically tailored for responses on the Bures-Wasserstein manifold. By deriving a degenerate V-statistic approximation with a limiting distribution as a weighted mixture of chi-squared variables, it provides a valid framework for analyzing complex data structures like gene co-expression networks in single-cell studies. The work advances the mathematical foundations necessary for handling non-Euclidean geometries in modern machine learning applications.
Test of partial effects for Frechet regression on Bures-Wasserstein manifolds
arXiv:2506.23487v2 Announce Type: replace-cross Abstract: We propose a novel test for assessing partial effects in Fr\'echet regression with responses lying on the Bures-Wasserstein manifold. Under the null hypothesis, we show that the statistic admits a degenerate V-statistic approximation whose limiting distribution is a weighted mixture of chi-squared random variables, with weights determined by the eigenvalues of an integral operator associated with a reproducing kernel Hilbert space (RKHS) kernel. We establish the asymptotic validity and consistency of the proposed test. Its finite-sample performance is examined through simulation studies. We apply the proposed test to study the effect of age, while controlling for other covariates, on gene co-expression structure in single-cell data.
Abstract:We propose a novel test for assessing partial effects in Fréchet regression with responses lying on the Bures-Wasserstein manifold. Under the null hypothesis, we show that the statistic admits a degenerate V-statistic approximation whose limiting distribution is a weighted mixture of chi-squared random variables, with weights determined by the eigenvalues of an integral operator associated with a reproducing kernel Hilbert space (RKHS) kernel. We establish the asymptotic validity and consistency of the proposed test. Its finite-sample performance is examined through simulation studies. We apply the proposed test to study the effect of age, while controlling for other covariates, on gene co-expression structure in single-cell data.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2506.23487 [stat.ML]
(or arXiv:2506.23487v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2506.23487 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 200 words
