Subsampling in ensemble Kalman inversion

Matei Hanu*, Jonas Latz, Claudia Schillings

*Corresponding author for this work

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Abstract

We consider the ensemble Kalman inversion (EKI) 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 EKI 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 EKI. 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).
Original languageEnglish
Article number094002
JournalInverse Problems
Volume39
Issue number9
Early online date28 Jul 2023
DOIs
Publication statusPublished - Sept 2023

Keywords

  • stochastic optimisation
  • piecewise-deterministic Markov process
  • particle system
  • inverse problems
  • data subsampling

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