XTrace: Making the most of every sample in stochastic trace estimation

@article{Epperly2023XTraceMT,
  title={XTrace: Making the most of every sample in stochastic trace estimation},
  author={Ethan N. Epperly and Joel A. Tropp and Robert J. Webber},
  journal={ArXiv},
  year={2023},
  volume={abs/2301.07825}
}
. The implicit trace estimation problem asks for an approximation of the trace of a square matrix, accessed via matrix–vector products (matvecs). This paper designs new randomized algorithms, XT RACE and XN YS T RACE , for the trace estimation problem by exploiting both variance reduction and the exchangeability principle. For a fixed budget of matvecs, numerical experiments show that the new methods can achieve errors that are orders of magnitude smaller than existing algorithms, such as the… 
1 Citations

Figures from this paper

Efficient error and variance estimation for randomized matrix computations

Two diagnostics are proposed: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation.