A Dilemma for Solomonoff Prediction

Neth, Sven

doi:10.1017/psa.2022.72

Cited by 5 publications

(2 citation statements)

References 33 publications

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“…Tere has been a lot of discussion in the statistics and philosophy communities regarding how to choose a Bayesian prior, and AIT promises to be one way to address this [58] (but see also reference [59] for a critique of this approach). Our work here is directly relevant to making practical implementations of this AIT answer to the Bayesian prior question.…”

Section: Discussionmentioning

confidence: 99%

Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications

Alaskandarani,

Dingle

2023

Complexity

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Developing new ways to estimate probabilities can be valuable for science, statistics, engineering, and other fields. By considering the information content of different output patterns, recent work invoking algorithmic information theory inspired arguments has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here, we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real-world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam’s razor, machine learning, and password guessing.

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Section: Discussionmentioning

confidence: 99%

Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications

Alaskandarani,

Dingle

2023

Complexity

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show abstract

“…There has been a lot of discussion in the statistics and philosophy communities regarding how to choose a Bayesian prior, and AIT promises to be one way to address this [56] (but see also ref. [57] for a critique of this approach). Our work here is directly relevant to making practical implementations of this AIT answer to the Bayesian prior question.…”

Section: Discussionmentioning

confidence: 99%

Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications

Alaskandarani¹,

Dingle²

2022

Preprint

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Developing new ways to estimate probabilities can be valuable for science, statistics, and engineering. By considering the information content of different output patterns, recent work invoking algorithmic information theory has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam's razor, machine learning, and password guessing.

show abstract