eprintid: 50330 rev_number: 14 eprint_status: archive userid: 1482 importid: 105 dir: disk0/00/05/03/30 datestamp: 2025-02-12 13:18:41 lastmod: 2025-02-19 11:01:16 status_changed: 2025-02-12 13:18:41 type: article metadata_visibility: show creators_name: Crespo, Marelys creators_name: Gadat, Sébastien creators_name: Gendre, Xavier creators_id: marelys.crespo-navas@ut-capitole.fr creators_id: sebastien.gadat@tse-fr.eu creators_id: xavier.gendre@math.univ-toulouse.fr creators_idrefppn: 283250607 creators_idrefppn: 080889433 creators_idrefppn: 13850265X creators_halaffid: 1002422 creators_halaffid: 1002422 creators_halaffid: 1954 title: Stochastic gradient langevin dynamics for (weakly) log-concave posterior distributions ispublished: pub subjects: subjects_ECO abstract: 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). date: 2024 date_type: published publisher: cElectronic Journal of Probability and Electronic Communications in Probability id_number: 10.1214/24-EJP1235 official_url: http://tse-fr.eu/pub/130251 faculty: tse divisions: tse keywords: Log-concave models , keywords: Stochastic gradient Langevin dynamics keywords: Weak convexity language: en has_fulltext: TRUE doi: 10.1214/24-EJP1235 view_date_year: 2024 full_text_status: restricted publication: Electronic Journal of Probability volume: Vol. 29 place_of_pub: Seattle, WA pagerange: 1-40 refereed: TRUE issn: 1083-6489 oai_identifier: oai:tse-fr.eu:130251 harvester_local_overwrite: volume harvester_local_overwrite: pending harvester_local_overwrite: creators_idrefppn harvester_local_overwrite: creators_halaffid harvester_local_overwrite: publisher harvester_local_overwrite: creators_id harvester_local_overwrite: place_of_pub harvester_local_overwrite: title harvester_local_overwrite: hal_id harvester_local_overwrite: hal_version harvester_local_overwrite: hal_url harvester_local_overwrite: hal_passwd oai_lastmod: 2025-02-10T08:00:05Z oai_set: tse site: ut1 hal_id: hal-04943092 hal_passwd: ebxs@d hal_version: 1 hal_url: https://hal.science/hal-04943092 citation: 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. document_url: https://publications.ut-capitole.fr/id/eprint/50330/1/Gadat_50330.pdf