Biological data analysis as an information theory problem: multivariable dependence measures and the shadows algorithm

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology
Nikita A Sakhanenko, David J Galas

Abstract

Information theory is valuable in multiple-variable analysis for being model-free and nonparametric, and for the modest sensitivity to undersampling. We previously introduced a general approach to finding multiple dependencies that provides accurate measures of levels of dependency for subsets of variables in a data set, which is significantly nonzero only if the subset of variables is collectively dependent. This is useful, however, only if we can avoid a combinatorial explosion of calculations for increasing numbers of variables.  The proposed dependence measure for a subset of variables, τ, differential interaction information, Δ(τ), has the property that for subsets of τ some of the factors of Δ(τ) are significantly nonzero, when the full dependence includes more variables. We use this property to suppress the combinatorial explosion by following the "shadows" of multivariable dependency on smaller subsets. Rather than calculating the marginal entropies of all subsets at each degree level, we need to consider only calculations for subsets of variables with appropriate "shadows." The number of calculations for n variables at a degree level of d grows therefore, at a much smaller rate than the binomial coefficient (n, d), but...Continue Reading

References

Dec 27, 1996·Cell·B R CairnsR D Kornberg
Jan 1, 2014·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·David J GalasTomasz Ignac
Feb 1, 2010·IEEE Transactions on Information Theory·David J GalasIlya Shmulevich

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Citations

Oct 14, 2017·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·Nikita A SakhanenkoDavid J Galas
Nov 30, 2018·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·Lisa UechiNikita A Sakhanenko
May 22, 2019·G3 : Genes - Genomes - Genetics·Nikita A SakhanenkoDavid J Galas
Jun 5, 2020·Circulation Research·Christoph D RauYibin Wang
Dec 18, 2019·Pharmacological Reviews·Jhana O HendrickxStuart Maudsley
Jan 5, 2021·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·David J GalasNikita A Sakhanenko
Jan 18, 2019·Entropy·David J Galas, Nikita A Sakhanenko
Apr 9, 2021·BMC Bioinformatics·James M Kunert-GrafDavid J Galas
Jul 1, 2019·G3 : Genes - Genomes - Genetics·Nikita A SakhanenkoDavid J Galas

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