Efficiency of Learned Indexes on Genome Spectra

Data structures on a multiset of genomic k-mers are at the heart of many bioinformatic tools. As genomic datasets grow in scale, the efficiency of these data structures increasingly depends on how well they leverage the inherent patterns in the data. One recent and effective approach is the use of learned indexes that approximate the rank function of a multiset using a piecewise linear function with very few segments. However, theoretical worst-case analysis struggles to predict the practical performance of these indexes. We address this limitation by developing a novel measure of piecewise-linear approximability of the data, called CaPLa (Canonical Piecewise Linear approximability). CaPLa builds on the empirical observation that a power-law model often serves as a reasonable proxy for piecewise linear-approximability, while explicitly accounting for deviations from a true power-law fit. We prove basic properties of CaPLa and present an efficient algorithm to compute it. We then demonstrate that CaPLa can accurately predict space bounds for data structures on real data. Empirically, we analyze over 500 genomes through the lens of CaPLa, revealing that it varies widely across the tree of life and even within individual genomes. Finally, we study the robustness of CaPLa as a measure and the factors that make genomic k-mer multisets different from random ones. Supplementary Material Software (Source Code): https://github.com/medvedevgroup/CaPLaarchivedatswh:1:dir:da45f156bdafa582fd16f04690ee49e184bf3590 FundingThis material is based upon work supported by the NSF under Grants No. DBI2138585 and OAC1931531. Research reported in this publication was supported by the National Institute Of General Medical Sciences of the NIH under Award Number R01GM146462. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH. GV was supported by the NextGenerationEU - National Recovery and Resilience Plan (Piano Nazionale di Ripresa e Resilienza, PNRR) - Project: "SoBigData.it - Strengthening the Italian RI for Social Mining and Big Data Analytics" - Prot. IR0000013 - Avviso n. 3264 del 28/12/2021