Efficient preconditioned stochastic gradient descent for estimation in latent variable models

TL;DR

This paper introduces an efficient preconditioned stochastic gradient algorithm for parameter estimation in complex latent variable models, addressing limitations of existing methods with proven convergence and demonstrated effectiveness in simulations.

Contribution

It proposes a novel preconditioned stochastic gradient method with Fisher information-based preconditioning, offering improved efficiency and convergence guarantees for latent variable models.

Findings

Effective in nonlinear mixed effects models

Performs well in stochastic block models

Converges under mild assumptions

Abstract

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.