4 papers
Regression analysis of distributional data through Multi-Marginal Optimal transport
Amirhossein Karimi, Tryphon T. Georgiou
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…
The Challenge of Small Data: Dynamic Mode Decomposition, Redux
Amirhossein Karimi, Tryphon T. Georgiou
We revisit the setting and the assumptions that underlie the methodology of Dynamic Mode Decomposition (DMD) in order to highlight caveats as well as potential measures of when the…
Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric
Amirhossein Karimi, Tryphon T. Georgiou
This manuscript introduces a regression-type formulation for approximating the Perron-Frobenius Operator by relying on distributional snapshots of data. These snapshots may represe…
Statistical learning in Wasserstein space
Amirhossein Karimi, Luigia Ripani, Tryphon T. Georgiou
We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast th…