Generic predictions of output probability based on complexities of inputs and outputs

Scientific Reports
Kamaludin DingleArd A Louis

Abstract

For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random sampling of inputs than complex outputs are. Here, we derive probability bounds that are based on the complexities of the inputs as well as the outputs, rather than just on the complexities of the outputs. The more that outputs deviate from the coding theorem bound, the lower the complexity of their inputs. Since the number of low complexity inputs is limited, this behaviour leads to an effective lower bound on the probability. Our new bounds are tested for an RNA sequence to structure map, a finite state transducer and a perceptron. The success of these new methods opens avenues for AIT to be more widely used.

References

Aug 9, 1993·Physical Review Letters·S Lloyd
Apr 25, 2002·Proceedings of the National Academy of Sciences of the United States of America·José M G VilarStanislas Leibler
Nov 26, 2002·BioEssays : News and Reviews in Molecular, Cellular and Developmental Biology·Walter Fontana
May 5, 2004·Proceedings of the National Academy of Sciences of the United States of America·David H MathewsDouglas H Turner
Jul 19, 2008·PLoS Computational Biology·Matthew C CowperthwaiteLauren Ancel Meyers
Oct 27, 2011·PloS One·Jacobo AguirreSusanna C Manrubia
May 29, 2015·Nature·Yann LeCunGeoffrey Hinton
Dec 15, 2015·Nature·Toby S CubittMichael M Wolf
Feb 24, 2018·Nature Communications·Kamaludin DingleArd A Louis

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Software Mentioned

AIT
Vienna package
RNA
FAdo

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