Distinguished Lecture by Prof. Charles Bouveyron (Inria Centre at Université Côte d’Azur) "Scaling Optimal Transport to High-Dimensional Gaussian Distributions with Application to Domain Adaptation"

Date and Time: October 26th, 2026, 16:00 -- 17:00 (JST)

Venue: Hybrid: Online and also at Uni. of Tokyo

Title: Scaling Optimal Transport to High-Dimensional Gaussian Distributions with Application to Domain Adaptation

Speaker: Prof. Charles Bouveyron (Inria Centre at Université Côte d’Azur)

Abstract:
Optimal transport (OT) has recently become very popular in machine learning, with application to several sub-fields such as clustering, dictionary learning and domain adaptation. However, OT is known to face challenges when dealing with high-dimensional data, such as images, texts or omics data. Most current OT approaches for high-dimensional situations rely on projections of the data or measures onto low-dimensional spaces, which inevitably results in information loss. In this work, we consider the case of high-dimensional Gaussian distributions with parsimonious covariance structures and lower intrinsic dimension. We exhibit a simplified closed-form expression of the 2-Wasserstein distance with an efficient and robust calculation procedure based on a low-dimensional decomposition of empirical covariance matrices, without relying on data projections. Furthermore, we provide a closed-form expression for the Monge map, which involves the exact calculation of the square-root and inverse square-root of the source distribution covariance matrix. This approach offers analytical and computational advantages, as demonstrated by our numerical experiments, which quantitatively evaluate these benefits in comparison to existing methods. In addition to being able to compute both the 𝑊22-distance and the transport map, our method can compete with model-free methods, in high dimension, even in the case of non-Gaussian distributions. Moreover, it reveals to be of particular interest in the context of unsupervised domain adaptation for supervised classification.

Short Bio:
Charles Bouveyron is a full Professor of Statistics at Université Côte d'Azur and the head of the INRIA research team MAASAI. He also holds a Chair on Artificial Intelligence of the Institut 3IA Côte d'Azur, one of the French AI institutes (IA Clusters). He serves as an associate editor for The Annals of Applied Statistics and he is the founding organizer of the series of Statlearn workshops. He was the director of Institut 3IA Côte d'Azur between 2021 and 2025.

His research interests include:
- Statistical learning (clustering, classification, regression) in high dimensions,
- Statistical learning on networks, texts, functional data and heterogeneous data,
- Deep latent variable models for clustering, representation leaning and matrix completion,
- Statistical optimal transport in high dimensions and for evolving data,
- Applications of statistical learning & AI to medicine, image analysis, ecology, astrophysics, humanities, ...