1. A color estimation system comprising: a correlation memory unit that stores a correlation model that accepts an input of an image or information of the image, and outputs an ink-color set that is a color combination of inks used in reproducing the image by printing; and a computer that extracts the ink-color set corresponding to a print image, which is an image to be printed, by providing an input of the print image or image information of the print image to the correlation model, wherein the correlation model is generated by performing machine learning that establishes a correlation between the image information and the ink-color set such that the ink-color set is outputted based on the image information, using a reference image of which the ink-color set necessary for printing is known in advance, wherein the image information refers to an image feature quantity defined as any one of: a histogram composed of numerical values corresponding to respective coordinates in a predetermined color space of each pixel in the image; numerical values corresponding to respective coordinates in a predetermined color space of a predetermined plurality of pixels in the image; and numerical values corresponding to respective coordinates in a predetermined color space of a representative color in a predetermined region, wherein the histogram is expressed by a function, the histogram having an envelope shape expressed by synthesizing a plurality of functions, the functions having respective coefficients used as the image feature quantity to estimate the outputted ink-color, wherein the computer is programmed to cause a display to display a selecting screen, the selecting screen permitting a user to change the color combination of the inks, and wherein the computer is programmed to receive a user's selection of a change to the color combination of the inks, and to cause inks to be generated which correspond to the outputted ink-color set.