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Documents authored by Koslicki, David

Document
DOI: 10.4230/LIPIcs.WABI.2025.16
Estimation of Substitution and Indel Rates via k-mer Statistics

Authors: Mahmudur Rahman Hera, Paul Medvedev, David Koslicki, and Antonio Blanca

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)

Abstract
Methods utilizing k-mers are widely used in bioinformatics, yet our understanding of their statistical properties under realistic mutation models remains incomplete. Previously, substitution-only mutation models have been considered to derive precise expectations and variances for mutated k-mers and intervals of mutated and non-mutated sequences. In this work, we consider a mutation model that incorporates insertions and deletions in addition to single-nucleotide substitutions. Within this framework, we derive closed-form k-mer-based estimators for the three fundamental mutation parameters: substitution, deletion rate, and insertion rates. We provide theoretical guarantees in the form of concentration inequalities, ensuring accuracy of our estimators under reasonable model assumptions. Empirical evaluations on simulated evolution of genomic sequences confirm our theoretical findings, demonstrating that accounting for insertions and deletions signals allows for accurate estimation of mutation rates and improves upon the results obtained by considering a substitution-only model. An implementation of estimating the mutation parameters from a pair of fasta files is available here: https://github.com/KoslickiLab/estimate_rates_using_mutation_model.git. The results presented in this manuscript can be reproduced using the code available here: https://github.com/KoslickiLab/est_rates_experiments.git.
Cite as

Mahmudur Rahman Hera, Paul Medvedev, David Koslicki, and Antonio Blanca. Estimation of Substitution and Indel Rates via k-mer Statistics. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rahmanhera_et_al:LIPIcs.WABI.2025.16,
  author =	{Rahman Hera, Mahmudur and Medvedev, Paul and Koslicki, David and Blanca, Antonio},
  title =	{{Estimation of Substitution and Indel Rates via k-mer Statistics}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.16},
  URN =		{urn:nbn:de:0030-drops-239422},
  doi =		{10.4230/LIPIcs.WABI.2025.16},
  annote =	{Keywords: k-mers, mutation rate, indel, alignment-free, estimation, substitution, insertion, deletion}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.6
Cosine Similarity Estimation Using FracMinHash: Theoretical Analysis, Safety Conditions, and Implementation

Authors: Mahmudur Rahman Hera and David Koslicki

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
Motivation. The increasing number and volume of genomic and metagenomic data necessitates scalable and robust computational models for precise analysis. Sketching techniques utilizing k-mers from a biological sample have proven to be useful for large-scale analyses. In recent years, FracMinHash has emerged as a popular sketching technique and has been used in several useful applications. Recent studies on FracMinHash proved unbiased estimators for the containment and Jaccard indices. However, theoretical investigations for other metrics, such as the cosine similarity, are still lacking. Theoretical contributions. In this paper, we present a theoretical framework for estimating cosine similarity from FracMinHash sketches. We establish conditions under which this estimation is sound, and recommend a minimum scale factor s for accurate results. Experimental evidence supports our theoretical findings. Practical contributions. We also present frac-kmc, a fast and efficient FracMinHash sketch generator program. frac-kmc is the fastest known FracMinHash sketch generator, delivering accurate and precise results for cosine similarity estimation on real data. We show that by computing FracMinHash sketches using frac-kmc, we can estimate pairwise cosine similarity speedily and accurately on real data. frac-kmc is freely available here: https://github.com/KoslickiLab/frac-kmc/.
Cite as

Mahmudur Rahman Hera and David Koslicki. Cosine Similarity Estimation Using FracMinHash: Theoretical Analysis, Safety Conditions, and Implementation. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hera_et_al:LIPIcs.WABI.2024.6,
  author =	{Hera, Mahmudur Rahman and Koslicki, David},
  title =	{{Cosine Similarity Estimation Using FracMinHash: Theoretical Analysis, Safety Conditions, and Implementation}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.6},
  URN =		{urn:nbn:de:0030-drops-206502},
  doi =		{10.4230/LIPIcs.WABI.2024.6},
  annote =	{Keywords: Hashing, sketching, FracMinHash, Min-Hash, k-mer, similarity, theory}
}
Document
DOI: 10.4230/LIPIcs.WABI.2022.15
WGSUniFrac: Applying UniFrac Metric to Whole Genome Shotgun Data

Authors: Wei Wei and David Koslicki

Published in: LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

Abstract
The UniFrac metric has proven useful in revealing diversity across metagenomic communities. Due to the phylogeny-based nature of this measurement, UniFrac has historically only been applied to 16S rRNA data. Simultaneously, Whole Genome Shotgun (WGS) metagenomics has been increasingly widely employed and proven to provide more information than 16S data, but a UniFrac-like diversity metric suitable for WGS data has not previously been developed. The main obstacle for UniFrac to be applied directly to WGS data is the absence of phylogenetic distances in the taxonomic relationship derived from WGS data. In this study, we demonstrate a method to overcome this intrinsic difference and compute the UniFrac metric on WGS data by assigning branch lengths to the taxonomic tree obtained from input taxonomic profiles. We conduct a series of experiments to demonstrate that this WGSUniFrac method is comparably robust to traditional 16S UniFrac and is not highly sensitive to branch lengths assignments, be they data-derived or model-prescribed.
Cite as

Wei Wei and David Koslicki. WGSUniFrac: Applying UniFrac Metric to Whole Genome Shotgun Data. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{wei_et_al:LIPIcs.WABI.2022.15,
  author =	{Wei, Wei and Koslicki, David},
  title =	{{WGSUniFrac: Applying UniFrac Metric to Whole Genome Shotgun Data}},
  booktitle =	{22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-243-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{242},
  editor =	{Boucher, Christina and Rahmann, Sven},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.15},
  URN =		{urn:nbn:de:0030-drops-170494},
  doi =		{10.4230/LIPIcs.WABI.2022.15},
  annote =	{Keywords: UniFrac, beta-diversity, Whole Genome Shotgun, microbial community similarity}
}
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