  Latent variable models are powerful tools for modeling complex phenomena
involving in particular partially observed data, unobserved variables or
underlying complex unknown structures. Inference is often difficult due to the
latent structure of the model. To deal with parameter estimation in the
presence of latent variables, well-known efficient methods exist, such as
gradient-based and EM-type algorithms, but with practical and theoretical
limitations. In this paper, we propose as an alternative for parameter
estimation an efficient preconditioned stochastic gradient algorithm. Our
method includes a preconditioning step based on a positive definite Fisher
information matrix estimate. We prove convergence results for the proposed
algorithm under mild assumptions for very general latent variables models. We
illustrate through relevant simulations the performance of the proposed
methodology in a nonlinear mixed effects model and in a stochastic block model.
