Kolmogorov Complexity/Solmanoff Induction and Minimum Message Length have been proven equivalent in their most-developed forms. Essentially, correct mathematical formalizations of Occam’s Razor are all the same thing.
The whole point is superfluous, because nobody is going to sit around and formally write out the axioms of these competing theories. It may be a correct argument, but it’s not necessarily convincing.
This is a pretty unhelpful way of justifying this sort of thing. Kolmogorv complexity doesn’t give a unique result. What programming system one uses as one’s basis can change things up to a constant. So simply looking at the fact that Solomonoff induction is equivalent to a lot of formulations isn’t really that helpful for this purpose.
Moreover, there are other formalizations of Occam’s razor which are not formally equivalent to Solomonoff induction. PAC learning is one natural example.
Kolmogorov Complexity/Solmanoff Induction and Minimum Message Length have been proven equivalent in their most-developed forms. Essentially, correct mathematical formalizations of Occam’s Razor are all the same thing.
The whole point is superfluous, because nobody is going to sit around and formally write out the axioms of these competing theories. It may be a correct argument, but it’s not necessarily convincing.
This is a pretty unhelpful way of justifying this sort of thing. Kolmogorv complexity doesn’t give a unique result. What programming system one uses as one’s basis can change things up to a constant. So simply looking at the fact that Solomonoff induction is equivalent to a lot of formulations isn’t really that helpful for this purpose.
Moreover, there are other formalizations of Occam’s razor which are not formally equivalent to Solomonoff induction. PAC learning is one natural example.