4 papers
On the Differential-Geometric Equivalence of Hellinger-Kantorovich and Cone-Wasserstein Spaces
Tristan Luca Saidi, Gonzalo Mena, Florian Gunsilius
The Hellinger-Kantorovich (HK) space provides a natural geometry for nonnegative measures with varying total mass, but its differential-geometric structure is less well understood…
On Model-Based Clustering With Entropic Optimal Transport
Gonzalo Mena
We develop a new methodology for model-based clustering. Optimizing the log-likelihood provides a principled statistical framework for clustering, with solutions found via the EM a…
Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems
Tristan Luca Saidi, Gonzalo Mena, Larry Wasserman +1
Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system…
Statistical Properties of Rectified Flow
Gonzalo Mena, Arun Kumar Kuchibhotla, Larry Wasserman
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, althoug…