Abstract

I will present some of my recent PhD research, where we reexamine unsupervised learning methods through the perspective of distributions using optimal transport. By drawing connections with the Gromov-Wasserstein (GW) problem, this research introduces a new comprehensive framework called distributional reduction. This framework encompasses both dimensionality reduction (DR) and clustering as special cases, enabling to address them jointly within a single optimization problem. Additionally, I will discuss the applications of the GW problem as a similarity measure between structured data represented as distributions, typically lying in different metric spaces, such as graphs of varying sizes. This will naturally lead to exploring research directions in graph generative modeling using GW.

Short biography:

I studied at École Polytechnique and hold a research master’s degree from École Normale Supérieure of Paris-Saclay. Currently, I am a third-year PhD student in the mathematics department at École Normale Supérieure de Lyon, supervised by Aurélien Garivier and Titouan Vayer. I have completed several internships, including positions at IBM Research Paris, where I worked on time series forecasting; Huawei Noah’s Ark Lab London, focusing on model-based reinforcement learning with normalizing flows; and Institut Pasteur, where I researched variational autoencoders (VAEs) for biosignals.