relation: https://publications.ut-capitole.fr/id/eprint/50330/ title: Stochastic gradient langevin dynamics for (weakly) log-concave posterior distributions creator: Crespo, Marelys creator: Gadat, Sébastien creator: Gendre, Xavier subject: B- ECONOMIE ET FINANCE description: In this paper, we investigate a continuous time version of the Stochastic Langevin Monte Carlo method, introduced in [39], that incorporates a stochastic sampling step inside the traditional overdamped Langevin diffusion. This method is popular in machine learning for sampling posterior distribution. We will pay specific attention in our work to the computational cost in terms of n (the number of observations that produces the posterior distribution), and d (the dimension of the ambient space where the parameter of interest is living). We derive our analysis in the weakly convex framework, which is parameterized with the help of the Kurdyka- Lojasiewicz (KL) inequality, that permits to handle a vanishing curvature settings, which is far less restrictive when compared to the simple strongly convex case. We establish that the final horizon of simulation to obtain an ε approximation (in terms of entropy) is of the order (d log(n)²)(1+r)² [log²(ε−1) + n²d²(1+r) log4(1+r)(n)] with a Poissonian subsampling of parameter n(d log²(n))1+r)−1, where the parameter r is involved in the KL inequality and varies between 0 (strongly convex case) and 1 (limiting Laplace situation). publisher: cElectronic Journal of Probability and Electronic Communications in Probability date: 2024 type: Article type: PeerReviewed format: text language: fr identifier: https://publications.ut-capitole.fr/id/eprint/50330/1/Gadat_50330.pdf identifier: Crespo, Marelys , Gadat, Sébastien and Gendre, Xavier (2024) Stochastic gradient langevin dynamics for (weakly) log-concave posterior distributions. Electronic Journal of Probability, Vol. 29. pp. 1-40. relation: http://tse-fr.eu/pub/130251 relation: 10.1214/24-EJP1235 identifier: 10.1214/24-EJP1235 doi: 10.1214/24-EJP1235 language: en