Inferring stellar metallicity and elemental abundances from kinematic and spectroscopic data using machine learning -- Implications for exoplanet host stars
(abridged) Elemental abundances of FGK stars can be derived routinely from high-resolution optical spectra, but this remains considerably more difficult for cooler stars. Machine-learning methods offer a practical route to infer otherwise inaccessible abundances from more widely available stellar data. We use a large APOGEE DR17 sample of red giant stars as the main training set and an independent HARPS sample of nearby FGK dwarfs for external validation. We benchmark several machine-learning regressors, optimise the strongest models, and analyse feature importance using gain-based metrics, permutation importance, single-feature models, and SHAP values. We also explored the prediction of C and O from Mg, Si, and [Fe/H], and derived simple empirical relations between selected abundance ratios (Fe/Si, Mg/Si, C/O, and Fe/O) and metallicity. Kinematic information alone recovers only a limited fraction of the variance in stellar metallicity, with a clear performance ceiling at RMSE $\sim$0.20 dex. The most informative predictor is the maximum vertical orbital excursion, $Z_{\max}$, followed by radial orbital parameters. When [Fe/H] is combined with kinematic information, the abundances of C, O, Mg, and Si are predicted significantly more accurately than with the baseline approximation $\mathrm{[X/H]}=\mathrm{[Fe/H]}$. In contrast, when predicting C and O from Mg, Si, and [Fe/H], most of the predictive power is already contained in the elemental abundances themselves, with Mg being the dominant contributor, and the addition of kinematic information provides little improvement. The trained models reproduce the main abundance trends associated with Galactic chemical evolution. We find that the slopes of the relations between Fe/Si, Mg/Si, C/O, and Fe/O and metallicity differ slightly between the HARPS and APOGEE samples, with fractional differences generally below 17\%.