Variants of Solomonoff induction: Difference between revisions

Revision as of 02:41, 31 March 2019

This page lists some variants of Solomonoff induction.

Source	Formula	Determinism	Type of machine used	Discrete vs continuous
LessWrong Wiki^[1]	$m(y_{0})=\sum _{p\in {\mathcal {P}}:U(p)=y_{0}}2^{-\ell (p)}$ where ${\mathcal {P}}$ 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 $y_{0}$ is finite
Scholarpedia discrete universal a priori probability^[2]	$m(x)=\sum _{p:U(p)=x}2^{-\ell (p)}$	deterministic?	prefix Turing machine	discrete
Scholarpedia continuous universal a priori probability^[2]	$M(x)=\sum _{p:U(p)=x*}2^{-\ell (p)}$		Monotone Turing machine	Continuous

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 | LessWrong Wiki<ref>https://wiki.lesswrong.com/wiki/Solomonoff_induction</ref> || <math>m(y_0) = \sum_{p \in \mathcal P : U(p) = y_0} 2^{-\ell(p)}</math> where <math>\mathcal P</math> 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 <math>y_0</math> is finite
 |-
-| 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> || 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
 |-
-| Scholarpedia continuous universal a priori probability<ref name="scholarpedia"/> ||
+| 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
 |}