We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the parameter space and the space of probability distributions and, contrary to other popular approaches, can be implemented when the latent variable takes values in discrete spaces. We provide a detailed theoretical analysis of both the mirror descent algorithm and its approximation via SMC. We experimentally show that the proposed algorithm outperforms standard expectation maximisation algorithms and is competitive with other popular methods for real-valued latent variables.

翻译：本文提出了一种基于镜像下降和序贯蒙特卡罗（SMC）的方法，用于在隐变量模型中执行联合参数推断和后验估计。该方法基于在参数空间和概率分布空间上最小化一个泛函，并且与其他流行方法不同，它可以在隐变量取值于离散空间时实现。我们对镜像下降算法及其通过SMC的近似进行了详细的理论分析。实验结果表明，所提出的算法优于标准的期望最大化算法，并且在实值隐变量问题上与其他流行方法具有竞争力。