Editing Algorithmic probability (section)

== History ==

Solomonoff invented the concept of algorithmic probability with its associated invariance theorem around 1960,<ref>Solomonoff, R., [http://world.std.com/~rjs/barc97.pdf "The Discovery of Algorithmic Probability"], ''Journal of Computer and System Sciences'', Vol. 55, No. 1, pp. 73-88, August 1997.</ref> publishing a report on it: "A Preliminary Report on a General Theory of Inductive Inference."<ref>Solomonoff, R., "[http://world.std.com/~rjs/z138.pdf A Preliminary Report on a General Theory of Inductive Inference]", Report V-131, Zator Co., Cambridge, Ma. (Nov. 1960 revision of the Feb. 4, 1960 report).</ref> He clarified these ideas more fully in 1964 with "A Formal Theory of Inductive Inference," Part I<ref>Solomonoff, R., "[http://world.std.com/~rjs/1964pt1.pdf A Formal Theory of Inductive Inference, Part I]". ''Information and Control'', Vol 7, No. 1 pp 1-22, March 1964.</ref> and Part II.<ref>Solomonoff, R., "[http://world.std.com/~rjs/1964pt2.pdf A Formal Theory of Inductive Inference, Part II]" ''Information and Control'', Vol 7, No. 2 pp 224–254, June 1964.</ref>

In terms of practical implications and applications, the study of bias in empirical data related to Algorithmic Probability emerged in the early 2010s.<ref>{{cite journal |last1=Soler-Toscano |first1=Fernando |last2=Zenil |first2=Hector |last3=Delahaye |first3=Jean-Paul |last4=Gauvrit |first4=Nicolas |title=Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines |journal=PLOS ONE |volume=9 |issue=5 |pages=74–85 |year=2014 |doi=10.1371/journal.pone.0096223 |doi-access=free |pmid=24787763 |pmc=4013017 |bibcode=2014PLoSO...996223S }}</ref> The bias found led to methods that combined algorithmic probability with perturbation analysis in the context of [[Exploratory causal analysis|causal analysis]]<ref>{{cite book |last1=Zenil |first1=Hector |last2=Kiani |first2=Narsis A. |last3=Tegnér |first3=Jesper |title=Algorithmic Information Dynamics: A Computational Approach to Causality with Applications to Living Systems |location=Cambridge |publisher=Cambridge University Press |year=2023 }}</ref><ref>{{cite journal |last1=Zenil |first1=H. |last2=Kiani |first2=N. A. |last3=Abrahão |first3=F. S. |last4=Tegnér |first4=J. N. |title=Algorithmic Information Dynamics |journal=Scholarpedia |volume=15 |issue=7 |year=2020 |pages=53143 |doi=10.4249/scholarpedia.53143 |doi-access=free |bibcode=2020SchpJ..1553143Z }}</ref><ref>{{cite journal |last1=Zenil |first1=Hector |last2=Kiani |first2=Narsis A. |last3=Zea |first3=Allan A. |last4=Tegnér |first4=Jesper |title=Causal deconvolution by algorithmic generative models |journal=Nature Machine Intelligence |volume=1 |issue=1 |year=2019 |pages=58–66 |doi=10.1038/s42256-018-0005-0 }}</ref> and non-differentiable [[Machine Learning]]<ref name="HernandezOrozco2021">{{Cite journal|last1=Hernández-Orozco|first1=Santiago|last2=Zenil|first2=Hector|last3=Riedel|first3=Jürgen|last4=Uccello|first4=Adam|last5=Kiani|first5=Narsis A.|last6=Tegnér|first6=Jesper|date=2021|title=Algorithmic Probability-Guided Machine Learning on Non-Differentiable Spaces|journal=Frontiers in Artificial Intelligence|volume=3|pages=1–20|doi=10.3389/frai.2020.567356|doi-access=free |pmid=33733213 |pmc=7944352 }}</ref>