4 papers
Non-asymptotic Tail Bounds for the Kostlan--Shub--Smale Field: Tensor PCA and Spherical -Spin Complexity
Jean-Marc Azaïs, Federico Dalmao, Yohann De Castro
This paper builds a hierarchy of explicit, non-asymptotic tail bounds for the supremum of the Kostlan--Shub--Smale (KSS) random field on the sphere, and applies it to two problems:…
Fast Spawn\&Prune (FS\&P): Global convergence of stochastic conic particle gradient descent via birth/death process
Yohann De Castro, Sébastien Gadat, Clément Marteau
We investigate the global optimization of the objective function arising in continuous sparse regression, specifically the Beurling LASSO (BLASSO), over the space of measures. Whil…
Gaussian Mixture Model with unknown diagonal covariances via continuous sparse regularization
Romane Giard, Yohann de Castro, Clément Marteau
This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ…
FastPart: Over-Parameterized Stochastic Gradient Descent for Sparse optimisation on Measures
Yohann De Castro, Sébastien Gadat, Clément Marteau
This paper presents a novel algorithm that leverages Stochastic Gradient Descent strategies in conjunction with Random Features to augment the scalability of Conic Particle Gradien…