Solomonoff Induction

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2025 Apr 16 14:4
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Edited
Edited
2025 Apr 16 14:8
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MDL
Solomonoff Induction considers all hypotheses as candidates, assigning higher weights to simpler hypotheses based on their
Kolmogorov Complexity
, providing a mathematical justification for
Occam's Razor
. For observed data, it evaluates the probability of all possible programs that could generate that data, with simpler programs being considered more likely. This implements an ideal Bayesian approach to predicting future data.
While theoretically powerful, it is computationally impossible to implement in practice since it requires considering all possible programs. Instead, this model serves as a theoretical limit and ideal standard for inference.
 
 
 
 
Solomonoff induction - LessWrong
Solomonoff induction is an ideal answer to questions like "What probably comes next in the sequence 1, 1, 2, 3, 5, 8?" or "Given the last three years of visual data from this webcam, what will this robot probably see next?" or "Will the sun rise tomorrow?" Solomonoff induction requires infinite computing power, and is defined by taking every computable algorithm for giving a probability distribution over future data given past data, weighted by their algorithmic simplicity, and updating those weights by comparison to the actual data. E.g., somewhere in the ideal Solomonoff distribution is an exact copy of you, right now, staring at a string of 1s and 0s and trying to predict what comes next - though this copy of you starts out with a very low weight in the mixture owing to its complexity. Since a copy of you is present in this mixture of computable predictors, we can prove a theorem about how well Solomonoff induction does compared to an exact copy of you; namely, Solomonoff induction commits only a bounded amount of error relative to you, or any other computable way of making predictions. Solomonoff induction is thus a kind of perfect or rational ideal for probabilistically predicting sequences, although it cannot be implemented in reality due to requiring infinite computing power. Still, considering Solomonoff induction can give us important insights into how non-ideal reasoning should operate in the real world. Additional reading: * https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_inductive_inference * http://lesswrong.com/lw/dhg/an_intuitive_explanation_of_solomonoff_induction/ * http://wiki.lesswrong.com/wiki/Solomonoff_induction
Solomonoff induction - LessWrong
 
 

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