The problem is that you don’t have time to follow the recipe.
In my view this is not the main practical problem with SI. In practice it doesn’t matter much that you can’t find the Kolmogorov complexity; you can still get closer and closer to it and as you do so you will get closer and closer to the truth.
The main practical problem with SI as a principle of statistics is that the Kolmogorov complexity is not an absolute quantity in the limited-data regime where most statistical analysis takes place. Imagine a psychologist who hands out N=400 surveys with 10 questions apiece, and each question has 8 possible answers. Then a naive encoding of the data set is 12,000 bits; this quantity is small compared to the Turing machine translation constants and so your estimate of the KC is entirely dependent on your choice of Turing machine.
The main practical problem with Solomonoff Induction surely is our lack of good quality computable approximations to it. If you don’t have much data, you can usually just gather some more data—there’s a whole world of it out there. It’s a trivial solution, but it resolves an awful lot of problems.
In my view this is not the main practical problem with SI. In practice it doesn’t matter much that you can’t find the Kolmogorov complexity; you can still get closer and closer to it and as you do so you will get closer and closer to the truth.
The main practical problem with SI as a principle of statistics is that the Kolmogorov complexity is not an absolute quantity in the limited-data regime where most statistical analysis takes place. Imagine a psychologist who hands out N=400 surveys with 10 questions apiece, and each question has 8 possible answers. Then a naive encoding of the data set is 12,000 bits; this quantity is small compared to the Turing machine translation constants and so your estimate of the KC is entirely dependent on your choice of Turing machine.
The main practical problem with Solomonoff Induction surely is our lack of good quality computable approximations to it. If you don’t have much data, you can usually just gather some more data—there’s a whole world of it out there. It’s a trivial solution, but it resolves an awful lot of problems.