Thibault Pautrel Presents a Paper at ICML 2026 in South Korea
Thibault Pautrel, a graduate of ENSAI’s Master’s program in Smart Data Science, presented the paper “Riemannian stochastic optimization for sufficient dimension reduction,” co-authored with François Portier, at the 43rd International Conference on Machine Learning (ICML), held in Seoul from July 6 to 11, 2026.
ICML, the International Conference on Machine Learning, is the leading international academic conference on machine learning and artificial intelligence.
Thibault Pautrel, who earned his Master for Smart Data Science in 2025, holds a Ph.D. in mathematics. He defended his doctoral dissertation (at IRMAR) on the zeros of polynomials with random coefficients in 2022.
Following his Master’s program, Thibault Pautrel joined the L2S Signals and Systems Laboratory (CentraleSupélec, Université Paris-Saclay) as a postdoctoral researcher, focusing on federated learning with parameters taking values in manifolds.
At the same time, Thibault worked with François Portier, a professor of statistics at CREST ENSAI and director of ENSAI’s Master for Smart Data Science, on a project involving dimensionality reduction in regression.
When there are many variables, regression models are difficult to estimate, and the accuracy of predictions is reduced compared to the standard case. In this context, Thibault Pautrel and François Portier proposed an improvement to the MAVE method, published in 2002. The proposed approach is based on nearest neighbors as well as a gradient descent method on the Stiefel manifold, thus combining the expertise of both researchers.
The project was accepted at ICML 2026, leading Thibault Pautrel to present the paper “Riemannian stochastic optimization for sufficient dimension reduction” at the conference.
Riemannian stochastic optimization for sufficient dimension reduction – Abstract
Sufficient dimension reduction (SDR) makes high-dimensional regression tractable by projecting the covariates onto a low-dimensional subspace that preserves the conditional mean of the response. Existing gradient-based estimators either operate in the ambient space and suffer from the curse of dimensionality, or localize in the reduced space at a per-outer-iteration cost at least quadratic in the sample size. We show that minimizers of the population Minimum Average Variance Estimation (MAVE) risk approximate the same Grassmannian target as the Outer Product of Gradients (OPG), and recast the empirical criterion as a smooth maximization on the Stiefel manifold with closed-form Riemannian gradient. The resulting algorithm, SMAVE, combines sparse projected-space nearest-neighbor localization with Riemannian stochastic gradient ascent. A simplified version comes with almost-sure convergence and a non-asymptotic rate matching the standard non-convex stochastic first-order scaling. Empirically, SMAVE matches or improves on RMAVE’s synthetic subspace recovery at moderate-to-high ambient dimension, and on four real datasets it uniformly improves over OPG and is competitive with or outperforms RMAVE at orders of magnitude lower runtime.
Learn more about Thibault Pautrel, François Portier, and research at ENSAI.