The population Monte Carlo (PMC) algorithm is a powerful adaptive importance sampling (AIS) methodology used for estimating expected values of random quantities w.r.t. some target probability distribution. At each iteration, a Markov transition kernel is used to propagate a set of particles. Importance weights of the particles are computed and then used to resample the particles that are most representative of the target distribution. At the end of the algorithm, the set of all particles and weights can be used to perform estimation. The resampling step is an adaptive mechanism of the PMC algorithm that allows for particles to locate the most significant regions of the sampling space. In this letter, we generalize the adaptation procedure of PMC sampling by providing a perspective based on stochastic optimization rather than resampling. The proposed method is more flexible than standard PMC as it allows the parameter adaptation to be resolved using any stochastic optimization method. We show that under certain conditions, the standard PMC algorithm is a special case of the proposed approach.

中文翻译：

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随机梯度种群蒙特卡罗

总体蒙特卡洛 (PMC) 算法是一种强大的自适应重要性采样 (AIS) 方法，用于估计随机量的期望值与某些目标概率分布。在每次迭代中，使用马尔可夫转换核来传播一组粒子。计算粒子的重要性权重，然后用于重新采样最能代表目标分布的粒子。在算法结束时，可以使用所有粒子和权重的集合进行估计。重采样步骤是 PMC 算法的一种自适应机制，它允许粒子定位采样空间的最重要区域。在这封信中，我们通过提供基于随机优化而不是重采样的视角来概括 PMC 采样的适应过程。所提出的方法比标准 PMC 更灵活，因为它允许使用任何随机优化方法解决参数适应问题。我们表明，在某些条件下，标准 PMC 算法是所提出方法的特例。