In this paper, we introduce a new algorithm for rare event estimation based on adaptive importance sampling. We consider a smoothed version of the optimal importance sampling density, which is approximated by an ensemble of interacting particles. The particle dynamics is governed by a McKean-Vlasov stochastic differential equation, which was introduced and analyzed in (Carrillo et al., Stud. Appl. Math. 148:1069-1140, 2022) for consensus-based sampling and optimization of posterior distributions arising in the context of Bayesian inverse problems. We develop automatic updates for the internal parameters of our algorithm. This includes a novel time step size controller for the exponential Euler method, which discretizes the particle dynamics. The behavior of all parameter updates depends on easy to interpret accuracy criteria specified by the user. We show in numerical experiments that our method is competitive to state-of-the-art adaptive importance sampling algorithms for rare event estimation, namely a sequential importance sampling method and the ensemble Kalman filter for rare event estimation.

翻译：本文提出了一种基于自适应重要性采样的罕见事件估计新算法。我们考虑最优重要性采样密度的平滑版本，该密度通过一组相互作用的粒子进行近似。粒子动力学由McKean-Vlasov随机微分方程控制，该方程在(Carrillo等人，《Stud. Appl. Math.》148:1069-1140, 2022)中针对贝叶斯反问题背景下后验分布的基于共识采样与优化问题被引入并进行了分析。我们开发了算法内部参数的自动更新方法，其中包括一种用于离散化粒子动力学的指数欧拉方法的新型时间步长控制器。所有参数更新的行为均取决于用户指定的易于理解的精度标准。数值实验表明，我们的方法在罕见事件估计方面与当前最先进的自适应重要性采样算法（即序贯重要性采样方法和用于罕见事件估计的集合卡尔曼滤波器）具有竞争力。