  The calculation of disconnected diagram contributions to physical signals is
a computationally expensive task in Lattice QCD. To extract the physical
signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix,
must be stochastically estimated. Because the variance of the stochastic
estimator is typically large, variance reduction techniques must be employed.
Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace
estimator by utilizing a telescoping sequence of estimators. Frequency
Splitting is one such method that uses a sequence of inverses of shifted
operators to estimate the trace of the inverse lattice Dirac operator, however
there is no a priori way to select the shifts that minimize the cost of the
multilevel trace estimation. In this article, we present a sampling and
interpolation scheme that is able to predict the variances associated with
Frequency Splitting under displacements of the underlying space time lattice.
The interpolation scheme is able to predict the variances to high accuracy and
therefore choose shifts that correspond to an approximate minimum of the cost
for the trace estimation. We show that Frequency Splitting with the chosen
shifts displays significant speedups over multigrid deflation, and that these
shifts can be used for multiple configurations within the same ensemble with no
penalty to performance.
