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

  1. https://wiki.lesswrong.com/wiki/Solomonoff_induction
  2. 2.0 2.1 Marcus Hutter; Shane Legg; Paul M.B. Vitanyi. "Algorithmic probability". Scholarpedia. 2007.
  3. Tom Florian Sterkenburg. "The Foundations of Solomonoff Prediction". February 2013.