  We formulate and solve a regression problem with time-stamped distributional
data. Distributions are considered as points in the Wasserstein space of
probability measures, metrized by the 2-Wasserstein metric, and may represent
images, power spectra, point clouds of particles, and so on. The regression
seeks a curve in the Wasserstein space that passes closest to the dataset. Our
regression problem allows utilizing general curves in a Euclidean setting
(linear, quadratic, sinusoidal, and so on), lifted to corresponding
measure-valued curves in the Wasserstein space. It can be cast as a
multi-marginal optimal transport problem that allows efficient computation.
Illustrative academic examples are presented.
