  As experimental searches for neutrinoless double-beta ($0\nu\beta\beta$)
decay are entering a new generation, with hopes to completely probe the
inverted mass hierarchy, the need for reliable nuclear matrix elements, which
govern the rate of this decay, is stronger than ever. Since a large discrepancy
in results is typically found with nuclear modela, a large unknown still exists
on the sensitivity of these experiments to the effective neutrino mass. We
consider this problem from a first-principles perspective, using the ab initio
valence-space in medium similarity renormalization group. In particular, we
study correlations of the $0\nu\beta\beta$-decay matrix elements in $^{76}$Ge
with other observables, such as the double Gamow-Teller giant resonance, from
34 input chiral interactions in an attempt to constrain our uncertainties and
investigate the interaction dependence of the nuclear matrix element.
