  The presence of certain elements within a star, and by extension its planet,
strongly impacts the formation and evolution of the planetary system. The
positive correlation between a host star's iron-content and the presence of an
orbiting giant exoplanet has been confirmed; however, the importance of other
elements in predicting giant planet occurrence is less certain despite their
central role in shaping internal planetary structure. We designed and applied a
machine learning algorithm to the Hypatia Catalog (Hinkel et a. 2014) to
analyze the stellar abundance patterns of known host stars to determine those
elements important in identifying potential giant exoplanet host stars. We
analyzed a variety of different elements ensembles, namely volatiles,
lithophiles, siderophiles, and Fe. We show that the relative abundances of
oxygen, carbon, and sodium, in addition to iron, are influential indicators of
the presence of a giant planet. We demonstrate the predictive power of our
algorithm by analyzing stars with known giant planets and found that they had
median 75% prediction score. We present a list of ~350 stars with no currently
discovered planets that have a $\geq$90% prediction probability likelihood of
hosting a giant exoplanet. We investigated archival HARPS data and found
significant trends that HIP62345, HIP71803, and HIP10278 host long-period giant
planet companions with estimated minimum $M_p\sin(i)$ values of 3.7, 6.8, and
8.5 M$_{J}$, respectively. We anticipate that our findings will revolutionize
future target selection, the role that elements play in giant planet formation,
and the determination of giant planet interior structure models.
