I have a general question that comes to my mind, I'm doing machine learning projects and I took a look at many datasets and worked with, mostly there are already famous datasets that everyone uses.
Now the question comes to my mind, let's say I decided to make my own dataset, is there a possibility that my data are so random so that no relationship exist between my inputs and outputs ?? this is interesting because if this is possible, then no machine learning model will achieve to find an inputs outputs relationship in the data and will fail to solve the regression or classification problem.
Moreover, is it mathematically possible that some values have absolutely no relationship between them? in other words, there is no function (linear or nonlinear) that can map those inputs to the outputs.
Now I thought about this problem and concluded that if there is a possibility for this, then it will likely happen in regression because maybe the target outputs are in the same range and the same features values can correspond to the same output values and that will confuse the machine learning model.
What are your thoughts on this? did you had this problem in your daily life as a machine learning engineer, data scientist or hobbyist?