A1319
Title: Frechet regression of multivariate distributions with nonparanormal transport
Authors: Junyoung Park - University of Michigan (United States) [presenting]
Abstract: Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which additionally encode dependence across univariate marginals, have received less attention and pose computational and statistical challenges. A new regression approach for multivariate distributional responses addresses these challenges by modeling distributions within the semiparametric nonparanormal family. By incorporating the nonparanormal transport (NPT) metric, an efficient closed-form surrogate for the Wasserstein distance, into the Frechet regression framework, the approach decomposes the problem into separate regressions of marginal distributions and their dependence structure, facilitating both efficient estimation and granular interpretation of predictor effects. Theoretical justification for NPT is provided, establishing its topological equivalence to the Wasserstein distance and proving that it mitigates the curse of dimensionality. Uniform convergence guarantees for regression estimators are proven, both when distributional responses are fully observed and when they are estimated from empirical samples, attaining fast convergence rates comparable to the univariate case. The utility of the method is demonstrated via simulations and an application to continuous glucose monitoring data.
