Inferring parameters of a latent variable model can be a daunting task when the conditional distribution of the latent variables given the observed ones is intractable. Variational approaches prove to be computationally efficient but, possibly, lack theoretical guarantees on the estimates, while sampling based solutions are quite the opposite. Starting from already available variational approximations, we define a first Monte Carlo EM algorithm to obtain maximum likelihood estimators, focusing on the Poisson log-normal model which provides a generic framework for the analysis of multivariate count data. We then extend this algorithm to the case of a composite likelihood in order to be able to handle higher dimensional count data.

翻译：当给定观测变量时，潜变量的条件分布难以处理时，推断潜变量模型的参数可能是一项艰巨的任务。变分方法在计算上高效，但可能缺乏对估计的理论保证，而基于采样的方法则恰恰相反。从已有的变分近似出发，我们首先定义了一种蒙特卡洛EM算法以获取最大似然估计，重点研究泊松对数正态模型，该模型为多元计数数据分析提供了通用框架。随后，我们将该算法扩展到复合似然情形，以便能够处理更高维度的计数数据。