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：本研究针对一类交互粒子系统展开分析，旨在实现用于优化潜变量模型参数的最大边际似然估计（MLE）过程。为此，我们提出一种连续时间交互粒子系统，该系统可视为扩展状态空间上的朗之万扩散过程，其中粒子数量相当于经典优化设置中逆温度参数的作用。基于朗之万扩散理论，我们根据粒子系统中的粒子数、算法迭代次数以及时间离散化分析中的步长参数，证明了最大边际似然估计量优化误差的非渐近集中界限。