6 papers
Uniform-in-time quantitative fluctuations of large scale interacting particle systems
Solesne Bourguin, Konstantinos Spiliopoulos
We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem fo…
Gaussian approximation on the Skorokhod space via Malliavin calculus and regularization
Solesne Bourguin, Simon Campese
We introduce a carré du champ operator for Banach-valued random elements, taking values in the projective tensor product, and use it to control the bounded Lipschitz distance betw…
Quantitative Fluctuation Analysis for Continuous-Time Stochastic Gradient Descent via Malliavin Calculus
Solesne Bourguin, Shivam S. Dhama, Konstantinos Spiliopoulos
In this paper, we establish a Quantitative Central Limit Theorem ({\sc qclt}) for the Stochastic Gradient Descent in Continuous Time ({\sc sgdct}) algorithm, whose parameter update…
A Caveat on Metrizing Convergence in Distribution on Hilbert Spaces
Federico Bassetti, Solesne Bourguin, Simon Campese +1
We consider Sobolev-type distances on probability measures over separable Hilbert spaces involving the Schatten- norms, which include as special cases a distance first introduce…
Non-central limit of densities of some functionals of Gaussian processes
Solesne Bourguin, Thanh Dang, Yaozhong Hu
We establish the convergence of the densities of a sequence of nonlinear functionals of an underlying Gaussian process to the density of a Gamma distribution. The key idea of our w…
Quantitative Error Bounds for Scaling Limits of Stochastic Iterative Algorithms
Xiaoyu Wang, Mikolaj J. Kasprzak, Jeffrey Negrea +2
Stochastic iterative algorithms, including stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD), are widely utilized for optimization and sampling in…