Variants of Solomonoff induction: Difference between revisions

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| Scholarpedia discrete universal a priori probability<ref name="scholarpedia">Marcus Hutter; Shane Legg; Paul M.B. Vitanyi. [http://www.scholarpedia.org/article/Algorithmic_probability "Algorithmic probability"]. 2007.</ref> || <math>m(x) = \sum_{p:U(p)=x} 2^{-\ell(p)}</math> || deterministic? || prefix Turing machine || discrete
| Scholarpedia discrete universal a priori probability<ref name="scholarpedia">Marcus Hutter; Shane Legg; Paul M.B. Vitanyi. [http://www.scholarpedia.org/article/Algorithmic_probability "Algorithmic probability"]. 2007.</ref> || <math>m(x) = \sum_{p:U(p)=x} 2^{-\ell(p)}</math> || deterministic? || prefix Turing machine || discrete
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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> || || 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> || deterministic? || Monotone Turing machine || Continuous
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Revision as of 02:46, 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] deterministic? prefix Turing machine discrete
Scholarpedia continuous universal a priori probability[2] deterministic? Monotone Turing machine Continuous

References

  1. https://wiki.lesswrong.com/wiki/Solomonoff_induction
  2. 2.0 2.1 Marcus Hutter; Shane Legg; Paul M.B. Vitanyi. "Algorithmic probability". 2007.