In practice no one honestly computes the complexity of models in any of the fields I am familiar with, such as physics, bio, chem etc. Sometimes they count the number of parameters/degrees of freedom, like in your example. In reality there is a dearth of models that explain observations and predict something new, interesting and testable, so the issue rarely arises.
Minimum message length fitting uses an approximation of K-complexity and gets used sometimes when people want to fit weird curves in a sort of principled way. But “real” Solomonoff induction is about feeding literally all of your sensory data into the algorithm to get predictions for the future, not just fitting curves.
So I guess I’d say that it’s possible to approximate K-complexity and use that in your prior for curve fitting, and people sometimes do that. But that’s not necessarily going to be your best estimate, because your best estimate is going to take into account all of the data you’ve already seen, which becomes impossible very quickly (even if you just want a controlled approximation).
In practice no one honestly computes the complexity of models in any of the fields I am familiar with, such as physics, bio, chem etc. Sometimes they count the number of parameters/degrees of freedom, like in your example. In reality there is a dearth of models that explain observations and predict something new, interesting and testable, so the issue rarely arises.
Minimum message length fitting uses an approximation of K-complexity and gets used sometimes when people want to fit weird curves in a sort of principled way. But “real” Solomonoff induction is about feeding literally all of your sensory data into the algorithm to get predictions for the future, not just fitting curves.
So I guess I’d say that it’s possible to approximate K-complexity and use that in your prior for curve fitting, and people sometimes do that. But that’s not necessarily going to be your best estimate, because your best estimate is going to take into account all of the data you’ve already seen, which becomes impossible very quickly (even if you just want a controlled approximation).