High-Dimensional Structure Theory Team Seminar (Talk by Christophe Quentin Valvason, University of Geneva)

An online seminar hosted by the High-Dimensional Structure Theory Team at RIKEN AIP, featuring Christophe Quentin Valvason of the University of Geneva. The talk, titled "Optimal Transport for Nonparametric Inference: Improving Confidence Intervals", addresses the difficulty of reliable statistical inference in small samples, where standard confidence procedures can deviate substantially from their nominal coverage. The speaker presents a method that recasts confidence interval construction as an optimal transport problem between a discrete source measure and an estimate of the sampling distribution. The talk covers finite-sample bounds on non-coverage probability tied to the geometry of the dual potential, asymptotic validity including consistency in the Hausdorff metric, a regularization view of why finite support stabilizes the construction, and simulation studies showing coverage closer to nominal than standard bootstrap procedures.