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.

翻译：潜变量模型是建模复杂现象（特别涉及部分观测数据、未观测变量或底层复杂未知结构）的有力工具。由于模型的潜在结构，推断通常面临困难。针对含潜变量的参数估计问题，现有梯度类算法和EM类算法等成熟方法虽有效但存在实践与理论上的局限性。本文提出一种高效的预处理随机梯度下降算法作为参数估计的替代方案。该方法基于正定Fisher信息矩阵估计实现预处理步骤。我们在非常一般的潜变量模型温和假设条件下证明了所提算法的收敛性。通过非线性混合效应模型和随机块模型的仿真实验，验证了该方法的性能表现。