Might be worth more explicitly noting in the post that P_sol and P_ap in fact define the same semimeasure over strings(up to a multiplicative factor) From a skim I was confused about this point “wait, is he saying that not only are alt-complexity and K-complexity different, but even define different probability distributions? That seems to contradict the universality of P_sol, doesn’t it....?”
Good idea, I now added the following to the opening paragraphs of the section doing the comparisons:
Importantly, due to Theorem 4, this means that the Solomonoff prior Psol and a priori prior Pap lead up to a constant to the same predictions on sequences. The advantages of the priors that we analyze are thus not statements about their induced predictive distributions.
Might be worth more explicitly noting in the post that P_sol and P_ap in fact define the same semimeasure over strings(up to a multiplicative factor) From a skim I was confused about this point “wait, is he saying that not only are alt-complexity and K-complexity different, but even define different probability distributions? That seems to contradict the universality of P_sol, doesn’t it....?”
Good idea, I now added the following to the opening paragraphs of the section doing the comparisons: