We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. In the case of large data sets, the Ensemble Kalman Inversion becomes computationally infeasible as the data misfit needs to be evaluated for each particle in each iteration. Here, randomised algorithms like stochastic gradient descent have been demonstrated to successfully overcome this issue by using only a random subset of the data in each iteration, so-called subsampling techniques. Based on a recent analysis of a continuous-time representation of stochastic gradient methods, we propose, analyse, and apply subsampling-techniques within Ensemble Kalman Inversion. Indeed, we propose two different subsampling techniques: either every particle observes the same data subset (single subsampling) or every particle observes a different data subset (batch subsampling).

翻译：我们考虑近期引入的集成卡尔曼反演方法，这是一种高效、无需梯度的优化方法，用于在反演场景中估计未知参数。当处理大规模数据集时，集成卡尔曼反演会因每次迭代中需针对每个粒子评估数据失配而变得计算不可行。在此背景下，随机梯度下降等随机算法通过每次迭代仅使用数据的随机子集（即子采样技术）已被证明能成功克服这一难题。基于对随机梯度方法连续时间表示的最新分析，我们在集成卡尔曼反演中提出、分析并应用了子采样技术。具体而言，我们提出了两种不同的子采样方案：所有粒子观测相同的数据子集（单子采样），或每个粒子观测不同的数据子集（批量子采样）。