How is it that Solomonoff Induction, and by extension Occam's Razor, is justified in the first place? Why is it that hypotheses with higher Kolmogorov complexity are less likely to be true than those with lower Kolmogorov complexity? If it is justified by that fact that it has "worked" in the past, does that not require Solomonoff induction to justify that has worked, in the sense that you need to verify that your memories are true, and thus requires circular reasoning?

See: You only need faith in two things and the comment on the binomial monkey prior (a theory which says that the 'past' does not predict the 'future').

You could argue that there exists a more fundamental assumption, hidden in the supposed rules of probability, about the validity of the evidence you're updating on. Here I can only reply that we're trying to explain the data regardless of whether or not it "is true," and point to the fact that you're clearly willing to act like this endeavor has value.

0entirelyuseless4yThere are more hypotheses with a high complexity than with a low complexity, so it is mathematically necessary to assign lower probabilities to high complexity cases than to low complexity cases (broadly speaking and in general -- obviously you can make particular exceptions) if you want your probabilities to sum to 1, because you are summing an infinite series, and to get it to come to a limit, the terms in the series must be generally decreasing.

New Philosophical Work on Solomonoff Induction

by vallinder 1 min read27th Sep 201611 comments


I don't know to what extent MIRI's current research engages with Solomonoff induction, but some of you may find recent work by Tom Sterkenburg to be of interest. Here's the abstract of his paper Solomonoff Prediction and Occam's Razor:

Algorithmic information theory gives an idealised notion of compressibility that is often presented as an objective measure of simplicity. It is suggested at times that Solomonoff prediction, or algorithmic information theory in a predictive setting, can deliver an argument to justify Occam's razor. This article explicates the relevant argument and, by converting it into a Bayesian framework, reveals why it has no such justificatory force. The supposed simplicity concept is better perceived as a specific inductive assumption, the assumption of effectiveness. It is this assumption that is the characterising element of Solomonoff prediction and wherein its philosophical interest lies.