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Will_Newsome comments on Open Problems Related to Solomonoff Induction - Less Wrong
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Comments (102)
Physics theories import low-complexity mathematical models. "Goddidit" imports complicated human notions of agency. Approximate explanations are fine if we can reason that their implicit complexity is low relative to their explanatory power (a relatively easily satisfied metric, after which competition between theories becomes the key factor).
In Solomonoff Induction, theories that don't explain data must contain that data raw.
Also keep in mind that algorithmic information/probability theory is actually quite hard to interpret correctly --- the basic, intuitive way to read meaning into the math is not quite the way to do it. cousin_it has a post or two correcting some intuitive errors of interpretation.
I found these:
Intuitive Explanation of Solomonoff Induction - lukeprog
Does Solomonoff always win? - cousin_it
K-complexity of everyday things - cousin_it
Solomonoff Induction, by Shane Legg - cousin_it
I would appreciate it if people could link me to more.
Alas, none of those are the relevant ones I think. I'm actually rather busy visiting home, so I can only justify certain comments to myself, but I hope someone provides the links.
For what it's worth, I'm a little skeptical of lukeprog's understanding of SI --- no offense to him meant, it's just I so happen to believe he made a rather big error when interpreting the math. On the other hand, cousin_it seems to be really on the ball here. Those are just my impressions; I'm a pretend philosopher, not a compsci dude. At any rate I think it'd be just dandy for cousin_it to check Luke's posts and share his impression or critiques.
Here's one I was thinking of:
The prior of a hypothesis does not depend on its complexity - cousin_it
(If I recall, Nesov's comment clearly demonstrates the important point.)
That post seems to mix together the concept of a prior with the concept of experience.
http://lesswrong.com/lw/328/description_complexity_an_apology_and_note_on/
Mentioning it anywhere except algorithmic information theory is a sign of confusion. This includes theology and parapsychology. Use just Bayes or, if you want to be all fancy, updateless-like decision theories. I love algorithmic probability to death but it's just not something you should use casually. Too many pitfalls.
Bayes requires a prior.
No one should ever need to discuss "priors". Focus on the likelihood ratio.
...but that's like comparing apples and cheese!