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 Frechet 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.

Source: arXiv cs.LG | 2026-09-01