TY  - JOUR
CY  - Seattle, WA
ID  - publications50330
UR  - http://tse-fr.eu/pub/130251
A1  - Crespo, Marelys
A1  - Gadat, Sébastien
A1  - Gendre, Xavier
N2  - 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).
VL  - Vol. 29
TI  - Stochastic gradient langevin dynamics for (weakly) log-concave posterior distributions
AV  - restricted
EP  - 40
Y1  - 2024///
PB  - cElectronic Journal of Probability and Electronic Communications in Probability
JF  - Electronic Journal of Probability
KW  - Log-concave models ,
KW  - Stochastic gradient Langevin dynamics
KW  - Weak convexity
SN  - 1083-6489
SP  - 1
ER  -