Inga Girshfeld, USC

Title: Wasserstein Regression Statistical Inference for Distribution Regression with Bures-Wasserstein Metrics

Abstract: Leveraging the structure of the Bures-Wasserstein space, which characterizes Gaussian measures through their means and covariance matrices, we derive a novel estimator for the regression map. The incorporation of a kernel function in the loss function assigns weights to source distributions based on a Bures-Wasserstein metric, effectively transforming the problem into a classical kernel regression-like framework. We prove consistency and establish asymptotic normality for the proposed estimator.