  The search for hydride compounds that exhibit high $T_c$ superconductivity
has been extensively studied. Within the range of binary hydride compounds, the
studies have been developed well including data-driven searches as a topic of
interest. Toward the search for the ternary systems, the number of possible
combinations grows rapidly, and hence the power of data-driven search gets more
prominent. In this study, we constructed various regression models to predict
$T_c$ for ternary hydride compounds and found the extreme gradient boosting
(XGBoost) regression giving the best performance. The best performed regression
predicts new promising candidates realizing higher $T_c$, for which we further
identified their possible crystal structures. Confirming their lattice and
thermodynamical stabilities, we finally predicted new ternary hydride
superconductors, YKH$_{12}$ [$C2/m$ (No.12), $T_c$=143.2 K at 240 GPa] and
LaKH$_{12}$ [$R\bar{3}m$ (No.166), $T_c$=99.2 K at 140 GPa] from first
principles.
