Recent color printing technologies based on the principle of revealing colors on pre-functionalized achromatic supports by laser irradiation offer advanced functionalities, especially for security applications. However, for such technologies, the color prediction is challenging, compared to classic ink-transfer printing systems. The spectral properties of the coloring materials modified by the lasers are not precisely known and may strongly vary, depending on the laser settings, in a nonlinear manner. We show in this study, through the example of the color laser marking (CLM) technology, based on laser bleaching of a mixture of pigments, that the combination of an adapted optical reflectance model and learning methods to get the model's parameters enables prediction of the spectral reflectance of any printable color with rather good accuracy. Even though the pigment mixture is formulated from three colored pigments, an analysis of the dimensionality of the spectral space generated by CLM printing, thanks to a principal component analysis decomposition, shows that at least four spectral primaries are needed for accurate spectral reflectance predictions. A polynomial interpolation is then used to relate RGB laser intensities with virtual coordinates of new basis vectors. By studying the influence of the number of calibration patches on the prediction accuracy, we can conclude that a reasonable number of 130 patches are enough to achieve good accuracy in this application.