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Redundancy-aware unsupervised ranking based on game theory: Ranking pathways in collections of gene sets

Author

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  • Chiara Balestra
  • Carlo Maj
  • Emmanuel Müller
  • Andreas Mayr

Abstract

In Genetics, gene sets are grouped in collections concerning their biological function. This often leads to high-dimensional, overlapping, and redundant families of sets, thus precluding a straightforward interpretation of their biological meaning. In Data Mining, it is often argued that techniques to reduce the dimensionality of data could increase the maneuverability and consequently the interpretability of large data. In the past years, moreover, we witnessed an increasing consciousness of the importance of understanding data and interpretable models in the machine learning and bioinformatics communities. On the one hand, there exist techniques aiming to aggregate overlapping gene sets to create larger pathways. While these methods could partly solve the large size of the collections’ problem, modifying biological pathways is hardly justifiable in this biological context. On the other hand, the representation methods to increase interpretability of collections of gene sets that have been proposed so far have proved to be insufficient. Inspired by this Bioinformatics context, we propose a method to rank sets within a family of sets based on the distribution of the singletons and their size. We obtain sets’ importance scores by computing Shapley values; Making use of microarray games, we do not incur the typical exponential computational complexity. Moreover, we address the challenge of constructing redundancy-aware rankings where, in our case, redundancy is a quantity proportional to the size of intersections among the sets in the collections. We use the obtained rankings to reduce the dimension of the families, therefore showing lower redundancy among sets while still preserving a high coverage of their elements. We finally evaluate our approach for collections of gene sets and apply Gene Sets Enrichment Analysis techniques to the now smaller collections: As expected, the unsupervised nature of the proposed rankings allows for unremarkable differences in the number of significant gene sets for specific phenotypic traits. In contrast, the number of performed statistical tests can be drastically reduced. The proposed rankings show a practical utility in bioinformatics to increase interpretability of the collections of gene sets and a step forward to include redundancy-awareness into Shapley values computations.

Suggested Citation

  • Chiara Balestra & Carlo Maj & Emmanuel Müller & Andreas Mayr, 2023. "Redundancy-aware unsupervised ranking based on game theory: Ranking pathways in collections of gene sets," PLOS ONE, Public Library of Science, vol. 18(3), pages 1-17, March.
  • Handle: RePEc:plo:pone00:0282699
    DOI: 10.1371/journal.pone.0282699
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    References listed on IDEAS

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    1. Stefano Moretti & Fioravante Patrone & Stefano Bonassi, 2007. "The class of microarray games and the relevance index for genes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 256-280, December.
    2. Celia Fontanillo & Ruben Nogales-Cadenas & Alberto Pascual-Montano & Javier De Las Rivas, 2011. "Functional Analysis beyond Enrichment: Non-Redundant Reciprocal Linkage of Genes and Biological Terms," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-10, September.
    3. Shinichi Nakagawa, 2004. "A farewell to Bonferroni: the problems of low statistical power and publication bias," Behavioral Ecology, International Society for Behavioral Ecology, vol. 15(6), pages 1044-1045, November.
    4. Antigoni Elefsinioti & Marit Ackermann & Andreas Beyer, 2009. "Accounting for Redundancy when Integrating Gene Interaction Databases," PLOS ONE, Public Library of Science, vol. 4(10), pages 1-9, October.
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