We study a class of interacting particle systems for implementing a marginal maximum likelihood estimation (MLE) procedure to optimize over the parameters of a latent variable model. To do so, we propose a continuous-time interacting particle system which can be seen as a Langevin diffusion over an extended state space, where the number of particles acts as the inverse temperature parameter in classical settings for optimisation. Using Langevin diffusions, we prove nonasymptotic concentration bounds for the optimisation error of the maximum marginal likelihood estimator in terms of the number of particles in the particle system, the number of iterations of the algorithm, and the step-size parameter for the time discretisation analysis.

翻译：我们研究了一类交互粒子系统，用于实现最大边缘似然估计过程，以优化潜变量模型的参数。为此，我们提出了一种连续时间交互粒子系统，可以看作是在扩展状态空间上的Langevin扩散，其中粒子数在经典设置中作为优化的逆温度参数。使用Langevin扩散，我们证明了在粒子系统中的粒子数、算法的迭代次数和时间离散化分析的步长参数方面，最大边缘似然估计器的优化误差的非渐近集中界。