Gabriel Rioux

About Me

I am a third-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, partial differential equations, 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 aspects of the Gaussian-smoothed Wasserstein distance, which is a modification of the standard Wasserstein distance obtained by smoothing out the input measures via convolution with a Gaussian measure. By smoothing out local irregularities in the input measures, the smoothed Wasserstein distance breaks the curse of dimensionality in statistical applications intrisic to the unsmoothed distance whilst preserving its useful topological structure.

Publications and Working Papers

• Z. Goldfeld, K. Kato, G. Rioux, and R. Sadhu: Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence. arXiv preprint arXiv:2207.08683, 2022, [arxiv].
• Z. Goldfeld, K. Kato, G. Rioux, and R. Sadhu: Statistical inference with regularized optimal transport. arXiv preprint arXiv:2205.04283, 2022, [arxiv].
• Z. Goldfeld, K. Kato, S. Nietert, and G. Rioux: Limit distribution theory for smooth p-Wasserstein distances. arXiv preprint arXiv:2203.00159, 2022, [arxiv].
• 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

• 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.