18 citations · 112 across the 31 of their papers we have counts for
4 papers · 1 filter
Geometry and barycenters in large $\CAT(κ)$ spaces
Yassine Boukhateb, Victor-Emmanuel Brunel, Austin J. Stromme
We study the geometry and resulting properties of Fréchet functions and barycenters in metric spaces with curvature bounded above by a positive constant in the sense of Alexandrov.…
Functional Central Limit Theorem for Stochastic Gradient Descent
Kessang Flamand, Victor-Emmanuel Brunel
We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a f…
Bernstein-von Mises theorem for log-concave posteriors
Victor-Emmanuel Brunel
We prove new, general versions of Bernstein-von Mises theorem for both well-specified and misspecified models when the log-likelihood is concave in the parameter and the prior dist…
On the continuity of geodesically convex functions on Riemannian manifolds
Victor-Emmanuel Brunel, Pierre Pansu
In this short note, we prove that all geodesically convex functions defined on a Riemannian manifold are continuous in the interior of their domain. This is a folklore result, but…