作者：Ö. Deniz Akyildiz Francesca Romana Crucinio Mark Girolami Tim Johnston Sotirios Sabanis
我们研究了一类相互作用的粒子系统，用于实现边际最大似然估计（MLE）过程，以优化潜变量模型的参数。为此，我们提出了一个连续时间相互作用的粒子系统，该系统可以被视为扩展状态空间上的Langevin扩散，其中粒子的数量在经典设置中作为逆温度参数进行优化。利用Langevin扩散，我们根据粒子系统中粒子的数量、算法的迭代次数和时间离散化分析的步长参数，证明了最大边际似然估计器优化误差的非症状浓度界。
We study a class of interacting particle systems for implementing a marginalmaximum likelihood estimation (MLE) procedure to optimize over the parametersof a latent variable model. To do so, we propose a continuous-time interactingparticle system which can be seen as a Langevin diffusion over an extendedstate space, where the number of particles acts as the inverse temperatureparameter in classical settings for optimisation. Using Langevin diffusions, weprove nonasymptotic concentration bounds for the optimisation error of themaximum marginal likelihood estimator in terms of the number of particles inthe particle system, the number of iterations of the algorithm, and thestep-size parameter for the time discretisation analysis.
论文链接：http://arxiv.org/pdf/2303.13429v1
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