Variants of Solomonoff induction: Difference between revisions
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| Scholarpedia continuous universal a priori probability<ref name="scholarpedia"/> || <math>M(x) = \sum_{p : U(p) = x*} 2^{-\ell(p)}</math> where the sum is over minimal programs || deterministic? || Monotone Turing machine || Continuous | | Scholarpedia continuous universal a priori probability<ref name="scholarpedia"/> || <math>M(x) = \sum_{p : U(p) = x*} 2^{-\ell(p)}</math> where the sum is over minimal programs || deterministic? || Monotone Turing machine || Continuous | ||
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| Sterkenburg (p. 22)<ref name="sterkenburg">Tom Florian Sterkenburg. "The Foundations of Solomonoff Prediction". February 2013.</ref> || | | Sterkenburg (p. 22)<ref name="sterkenburg">Tom Florian Sterkenburg. "The Foundations of Solomonoff Prediction". February 2013.</ref> || <math>P_{\mathrm{I}}(\sigma) = \lim_{n\to\infty} \frac{|T_{\sigma,n}|}{T_n}</math> || || || | ||
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Revision as of 02:52, 31 March 2019
This page lists some variants of Solomonoff induction.
For determinism, I think "deterministic" is the same as "Solomonoff prior" and "stochastic" is the same as "universal mixture".
For discrete vs continuous, I think this just means whether the prior we define is over finite strings or over infinite sequences (where we want to know the probability of an infinite sequence starting with a given finite string).
Source | Formula | Determinism | Type of machine used | Discrete vs continuous |
---|---|---|---|---|
LessWrong Wiki[1] | where is the set of self-delimiting programs | Deterministic | Page doesn't say, but uses self-delimiting programs and it's discrete, so prefix Turing machine? | Discrete because the output string is finite |
Scholarpedia discrete universal a priori probability[2] | where the sum is over halting programs | deterministic? | prefix Turing machine | discrete |
Scholarpedia continuous universal a priori probability[2] | where the sum is over minimal programs | deterministic? | Monotone Turing machine | Continuous |
Sterkenburg (p. 22)[3] |
References
- ↑ https://wiki.lesswrong.com/wiki/Solomonoff_induction
- ↑ 2.0 2.1 Marcus Hutter; Shane Legg; Paul M.B. Vitanyi. "Algorithmic probability". Scholarpedia. 2007.
- ↑ Tom Florian Sterkenburg. "The Foundations of Solomonoff Prediction". February 2013.