Gabriel Rioux

About Me

I am a fourth-year Ph.D. candidate at Cornell University's Center for Applied Mathematics working under the supervision of Ziv Goldfeld. Previously, I studied at McGill University, earning a B.Sc. in honors Mathematics and Physics in 2019 and a M.Sc. in Mathematics and Statistics in 2020 under the supervision of Prof. Rustum Choksi and Prof. Tim Hoheisel. The subject of my Master's thesis was applying the maximum entropy on the mean method to the problem of image deblurring.

Research Interests

My research interests lie broadly in optimization, mathematical statistics, and probability. I am particularly interested in the interplay between these subjects, and hence, have recently been working on problems in optimal transportation.

My most recent work has focused on studying statistical and computational aspects of the Gromov-Wasserstein distance, which is a figure of merit for comparing the inner structure of metric measure spaces. Indeed, it defines a metric on the space of metric measure spaces modulo isometries.

Its definition is akin to the standard optimal transport problem with the important distinction that the underlying objective is non-convex in general (as opposed to the linear optimal transport problem). As such, principled analysis of the Gromov-Wasserstein distance requires new techniques, and many standard results from optimal transport (e.g. duality and existence of transport maps) do not yet have a direct analogue.

Publications and Working Papers

• G. Rioux, Z. Goldfeld, and K. Kato: Entropic Gromov-Wasserstein Distances: Stability and Algorithms. arXiv preprint arXiv:2306.00182, 2023, [arxiv].
• Z. Goldfeld, K. Kato, G. Rioux, and R. Sadhu: Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence. Electronic Journal of Statistics, 18(1), 2024, pp.980-1041. [arxiv, journal link ].
• Z. Goldfeld, K. Kato, G. Rioux, and R. Sadhu: Statistical inference with regularized optimal transport. Information and Inference: A Journal of the IMA, 13(1), 2024. [arxiv, journal link].
• Z. Goldfeld, K. Kato, S. Nietert, and G. Rioux: Limit distribution theory for smooth p-Wasserstein distances. Annals of Applied Probability, 34(2), 2024, pp.2447-2487, [arxiv, journal link].
• G. Rioux, R. Choksi, T. Hoheisel, C. Scarvelis, and P. Maréchal: The Maximum Entropy on the Mean Method for Image Deblurring. Inverse Problems 37, 2021 (29 pp.), [arxiv, journal link].
• G. Rioux, C. Scarvelis, R. Choksi, T. Hoheisel, and P. Maréchal: Blind Deblurring of Barcodes via Kullback-Leibler Divergence. IEEE Transactions on Pattern Analysis and Machine Intelligence 43(1), 2021, pp.77-88, [journal link].

Talks

• July 2020: Maximum Entropy on the Mean Image Deblurring via Fenchel Duality, presented at a Montréal Machine Learning and Optimization (MTL MLOpt) internal meeting [slides].

Awards and Fellowships

• 2022-2025: Natural Sciences and Engineering Research Council of Canada (NSERC) Postgraduate Scholarship - Doctoral (PGS D) recipient.
• 2019-2020: Natural Sciences and Engineering Research Council of Canada (NSERC) Alexander Graham Bell Canada Graduate Scholarship - Master's (CGS M) recipient.
• 2019-2020: Kenneth Eade Fellow.
• Fall 2018: McGill University Undergraduate Research Conference Poster Presentation 1st Prize in Computational and Mathematical Sciences Category.
• Summer 2018: McGill University Science Undergraduate Research Award (SURA) Recipient.

Teaching

• Spring 2024: Teaching Assistant, Fundamentals of Machine Learning, Cornell University.
• Fall 2023: Teaching Assistant, Information Theory for Data Transmission, Security, and Machine Learning , Cornell University.
• Fall 2021: Teaching Assistant, Introduction to Differential Equations, Cornell University.
• Spring 2021: Teaching Assistant, Introduction to Partial Differential Equations, Cornell University.
• Fall 2020: Teaching Assistant, Differential Equations for Engineers, Cornell University.