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Handbook of Statistical Bioinformatics pp 389–404Cite as

Liquid Association and Related Ideas in Quantifying Changes in Correlation

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Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

This chapter describes a novel statistical concept of a ternary relationship between variables in a complex data system, coined ‘liquid association’ (LA) by Li (Proc Natl Acad Sci U S A 99(16):16875–16880, 2002). LA describes how variation in the pattern of association between a pair of variables, including its sign and strength, is mediated by a third variable from the background. LA is introduced because despite the many successful applications of similarity based analysis on microarray data, numerous cases where the functional association between genes is known from the literature (confirmed by experiments) but the statistical correlation from the corresponding expression data is practically zero also exist. Other than the noises in the microarray data, a deeper reason may be the biological complexity of the cellular system and the hidden components, which are not directly measured by gene expression, such as multiple functions of a protein, varying cellular oxidization-reduction states, fluctuating hormone levels or other cellular signals and so on.

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Author information

Authors and Affiliations

  1. Institute of Statistical Science, Academia Sinica Department of Statistics, UCLA, Los Angeles, USA

    Ker-Chau Li

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  1. Ker-Chau Li
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Correspondence to Ker-Chau Li .

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Editors and Affiliations

  1. , Institute of Statistics, National Chiao Tung University, Ta Hsueh Road 1001, Hsinchu, 30050, Taiwan, Taiwan R.O.C.

    Henry Horng-Shing Lu

  2. , Department of Empirical Inference, MPI for Intelligent Systems, Spemannstraße 38, Tübingen, 72076, Germany

    Bernhard Schölkopf

  3. School of Medicine, Dept. Epidemiology & Public Health, Yale University, College Street 60, New Haven, 06520, Connecticut, USA

    Hongyu Zhao

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© 2011 Springer-Verlag Berlin Heidelberg

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Li, KC. (2011). Liquid Association and Related Ideas in Quantifying Changes in Correlation. In: Lu, HS., Schölkopf, B., Zhao, H. (eds) Handbook of Statistical Bioinformatics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16345-6_19

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