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Debiasing FracMinHash and deriving confidence intervals for mutation rates across a wide range of evolutionary distances

Mahmudur Rahman Hera, N. Tessa Pierce-Ward, View ORCID ProfileDavid Koslicki
doi: https://doi.org/10.1101/2022.01.11.475870
Mahmudur Rahman Hera
1Department of Computer Science and Engineering, The Pennsylvania State University
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N. Tessa Pierce-Ward
2Department of Population Health and Reproduction, University of California, Davis
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David Koslicki
1Department of Computer Science and Engineering, The Pennsylvania State University
3Department of Biology, The Pennsylvania State University
4Huck Institutes of the Life Sciences, The Pennsylvania State University
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  • ORCID record for David Koslicki
  • For correspondence: dmk333@psu.edu
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Abstract

Sketching methods offer computational biologists scalable techniques to analyze data sets that continue to grow in size. MinHash is one such technique that has enjoyed recent broad application. However, traditional MinHash has previously been shown to perform poorly when applied to sets of very dissimilar sizes. FracMinHash was recently introduced as a modification of MinHash to compensate for this lack of performance when set sizes differ. While experimental evidence has been encouraging, FracMinHash has not yet been analyzed from a theoretical perspective. In this paper, we perform such an analysis and prove that while FracMinHash is not unbiased, this bias is easily corrected. Next, we detail how a simple mutation model interacts with FracMinHash and are able to derive confidence intervals for evolutionary mutation distances between pairs of sequences as well as hypothesis tests for FracMinHash. We find that FracMinHash estimates the containment of a genome in a large metagenome more accurately and more precisely when compared to traditional MinHash, and the confidence interval performs significantly better in estimating mutation distances. A python-based implementation of the theorems we derive is freely available at https://github.com/KoslickiLab/mutation-rate-ci-calculator. The results presented in this paper can be reproduced using the code at https://github.com/KoslickiLab/ScaledMinHash-reproducibles.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • Update citation 15, typo fix "S"->"s" and other such minor changes.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license.
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Posted January 14, 2022.
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Debiasing FracMinHash and deriving confidence intervals for mutation rates across a wide range of evolutionary distances
Mahmudur Rahman Hera, N. Tessa Pierce-Ward, David Koslicki
bioRxiv 2022.01.11.475870; doi: https://doi.org/10.1101/2022.01.11.475870
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Debiasing FracMinHash and deriving confidence intervals for mutation rates across a wide range of evolutionary distances
Mahmudur Rahman Hera, N. Tessa Pierce-Ward, David Koslicki
bioRxiv 2022.01.11.475870; doi: https://doi.org/10.1101/2022.01.11.475870

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