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RR~Lyrae variables are widely used tracers of Galactic halo structure andkinematics, but they can also serve to constrain the distribution of the oldstellar population in the Galactic bulge. With the aim of improving theirnear-infrared photometric characterization, we investigate their near-infraredlight curves, as well as the empirical relationships between their light curveand metallicities using machine learning methods. We introduce a new, robustmethod for the estimation of the light-curve shapes, and hence the averagemagnitudes of RR~Lyrae variables in the $K_\mathrm{S}$ band, by utilizing thefirst few principal components (PCs) as basis vectors, obtained from the PCanalysis of a training set of light curves. Furthermore, we use the amplitudesof these PCs to predict the light-curve shape of each star in the $J$-band,allowing us to precisely determine their average magnitudes (hence colors),even in cases where only one $J$ measurement is available. Finally, wedemonstrate that the $K_\mathrm{S}$-band light-curve parameters of RR~Lyraevariables, together with the period, allow the estimation of the metallicity ofindividual stars with an accuracy of $\sim 0.2 - 0.25$ dex, providing valuablechemical information about old stellar populations bearing RR~Lyrae variables.The methods presented here can be straightforwardly adopted for other classesof variable stars, bands, or for the estimation of other physical quantities.

A Data-driven Study of RR Lyrae Near-IR Light Curves: Principal Component Analysis, Robust Fits, and Metallicity Estimates