I thought that overfitting referred to the color processing needed to convert a raw camera image to a standardized color representation. The more patches you record, the more confidence you can have in knowing the camera response (?) and the more parameters you could (in principle, at least) use in that color processing.
As I understand it, overfitting is where you have too many parameters for the number of data points, or more generally, when the model you are fitting is more complex than the reality of the data. You know you are overfitting when the model predicts the test data exactly, including noise, and when validation data is consistently fit worse than with fewer parameters.
I can't see how using more test colors will lead to overfitting if you use the same simple model.
I understand the simplicity of having a 3x3 linear matrix, but why limit oneself to that if there is sufficient data to do a more complex correction?
But what more complex correction makes logical sense? Sure, I think it would make a lot of sense to carefully linearize the raw data beforehand, and this linearization could be implemented as 3x or 4x 1D LUTs. You can make this as complicated as needed, attempting to control fixed pattern noise and so forth. But the more linear you make the data, the easier the rest is going to be. Fitting of this data is conceptually different from fitting the color data, as presumably it is objective without aesthetic judgment involved.
Even when using 3D LUTs, which can be complex with many variables, linearizing first allows the use of much simpler 3D LUTs.
But
why are 3D LUTs used? Besides for linearizing data, they are used for applying gamma curves, conversion to standard color spaces and most especially for creative control in color grading. So one data construct is handing many logically independent actions. Most of these actions are not statistical in nature, and so don't need to participate in the fitting of color data.
But what if you strip out all of the non statistical stuff that can be handled separately? What's left is the bare effects of the three color filters, which are linear, and the only operation that make sense—to me, at least—with this data is a 3x3 linear matrix.
After this process, you are left with device metamerism errors, which are irreducible and ultimately uncorrectable. You can attempt to adjust some metamers to match exactly, but lose other metamers in the process. But that's a judgement call: you have inevitable errors in color and you have to come up with a satisfactory method of distributing those errors.
Sure, there are other adjustments, such as making colors more pleasing, but again I think that is best done separately instead of part of the calibrated basic color conversion, which is the only part of the process which requires an intrinsically statistical approach.
