Research

I work at the intersection of Statistics, Machine Learning and Geometry. Recently, I have studied the barycenter estimation problem. My current research looks at ways geometrical considerations (such as synthetic curvature bounds) can inform the performance of randomized (PAC Bayesian) estimators.

Links

• arxiv
• Google Scholar

Publications

• Online learning with exponential weights in metric spaces. Daria Demidova and Quentin Paris (Preprint)
• Jensen’s inequality in geodesic spaces with lower bounded curvature. Daria Demidova and Quentin Paris (Preprint)
• Fast Convergence of Empirical Barycenters in Alexandrov Spaces and the Wasserstein Space. Thibaut Le Gouic, Quentin Paris, Philippe Rigollet, Austin J. Stromme. Journal of the European Mathematical Society, Vol. 25(6), p.2229-2250 (2023)
• Empirical variance minimization with applications in variance reduction and optimal control. Denis Belomestny, Leonid Iosipoi, Quentin Paris, Nikita Zhivotovskiy. Bernoulli. Vol. 28(2), p.1382-1407 (2022)
• Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendible geodesics. Adil Ahidar-Coutrix, Thibaut Le Gouic and Quentin Paris. Probability Theory and Related Fields, Vol. 177, p.323–368 (2020)
• On the occupancy problem for a regime switching model. Michael Grabchak, Mark Kelbert and Quentin Paris. Journal of Applied Probability, Vol. 57(1), p.53-77 (2020)
• A notion of stability for k-means clustering. Thibaut Le Gouic and Quentin Paris. Electronic Journal of Statistics, Vol. 12(2), p.4239-4263 (2018)
• On the prediction loss of the lasso in the partially labeled setting. Pierre Bellec, Arnak Dalalyan, Edwin Grappin and Quentin Paris. Electronic Journal of Statistics, Vol. 12(2), p.3443–3472 (2018)
• On the exponentially weighted aggregate with the Laplace prior. Arnak Dalalyan, Edwin Grappin and Quentin Paris. The Annals of Statistics, Vol. 46(5), p.2452-2478 (2018)
• Finite sample properties of the mean occupancy counts and probabilities. Geoffrey Decrouez, Michael Grabchak and Quentin Paris. Bernoulli, Vol. 24(3), p.1910-1941 (2018)
• Cox process functional learning. Gérard Biau, Benoit Cadre and Quentin Paris. Statistical Inference for Stochastic Processes, Vol. 18, p.1-21 (2015)
• Minimax adaptive dimension reduction for regression. Quentin Paris. Journal of Multivariate Analysis, Vol. 128, p.186-202 (2014)
• On Hölder fields clustering. Benoit Cadre and Quentin Paris. TEST, Vol. 21, p.301–316 (2012)