I hope you can help me with your expertise and breadth of knowledge for a problem that I will try to articulate as best as possible :)
Context: For an object, I can calculate n (in my case 9) features that determine derived features. One random example would be an image (object) and its features, e.g., how well it can be compressed, or a contrast score, or how many edges can be found, etc. etc. So far so good, but now the dimensions are not necessarily uncorrelated/linear independent. This could mean that a high value in one dimension can imply a high value in another dimension or a low value or constraint the value ranges. Illustrative example: An image that can be poorly compressed is showing most likely a high variance in terms of the color or gradients. (I'm totally making this up).
Problem: Now imagine that I want to "produce" an object generator, which can produce all these objects for me depending on the location in the HD space. Side note, this can be easily done with a GAN, variational autoencoders, or some other AI models. However, my challenge is to ensure that I have "captured" the entire functional feature space for the AI model learning step. But, how can I be certain that I have sampled the space (enough) if I'm not even clear how the functional dependencies are between the dimensions look like? On top of that, even if I had the correlation scores between the dimensions, which insane mathematical optimizer takes this as an input to tell me how the HD space "looks like"?
A rather vague mathematical description of the problem would be that I have an n-dimensional space, whose dimensions do not form an orthonormal basis. The dimensions are not (necessarily) linear independent, and their dependencies cannot easily/fully derived. How can I (experimentally) determine the possible solution space? Which mathematical problem shares (at least some) similarities? Which math subdiscipline deals with those kinds of problems?
One more thing: I don't expect full-fledged a solution of any sort, but only pointers.
THANK YOU SO MUCH!!!!