Subsampling in ensemble Kalman inversion

TL;DR

This paper introduces subsampling techniques for Ensemble Kalman Inversion to improve computational efficiency when handling large datasets, inspired by stochastic gradient methods, and analyzes their effectiveness.

Contribution

It proposes and analyzes two novel subsampling methods for Ensemble Kalman Inversion, enhancing scalability for large data problems.

Findings

Single subsampling reduces computational cost.

Batch subsampling maintains accuracy with smaller data subsets.

Methods are theoretically analyzed and practically demonstrated.

Abstract

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).