64th ISI World Statistics Congress - Ottawa, Canada

64th ISI World Statistics Congress - Ottawa, Canada

Distributional Regression with Optimal Transports

Author

HM
Hans-Georg Müller

Co-author

  • C
    Changbo Zhu

Conference

64th ISI World Statistics Congress - Ottawa, Canada

Format: IPS Abstract

Keywords: hilbert-sphere, random-objects, spherical-data, transport-algebra, wasserstein

Session: IPS 260 - Modern functional data analysis

Tuesday 18 July 2 p.m. - 3:40 p.m. (Canada/Eastern)

Abstract

Distributional data have become more visible and this has led to the emerging field of distributional data analysis, which provides tools for the analysis of samples of distributions. Distributional data can be viewed as a special type of random objects and they pose specific challenges: Densities and distributions do not form a vector space and they need to be estimated from the samples that they generate. For one-dimensional distributions the Wasserstein metric has become popular due to its inherent connection with optimal transport and the often convincing statistical performance in applications. This has led to the development of Wasserstein regression and other extrinsic approaches for distributional regression. An intrinsic approach can be based on a transport algebra, providing an alternative to extrinsic modeling for distribution-on-distribution regression. This also leads to an autoregressive optimal transport model. Especially for samples of multivariate distributions other metrics are also of interest, especially the Fisher-Rao metric, which corresponds to the geodesic distance on the Hilbert sphere. Adopting this metric motivates to study spherical regression and autoregressive spherical models, which can be based on rotations that provide optimal transports on the Hilbert sphere. Spherical regression models are also applicable for compositional and directional data. This talk is based on joint work with Changbo Zhu, Notre Dame University.