Proving sequence aligners can guarantee accuracy in almost <i>O</i> ( <i>m</i> log <i>n</i> ) time through an average-case analysis of the seed-chain-extend heuristic
Bibliographic record
Abstract
Seed-chain-extend with k -mer seeds is a powerful heuristic technique for sequence alignment used by modern sequence aligners. Although effective in practice for both runtime and accuracy, theoretical guarantees on the resulting alignment do not exist for seed-chain-extend. In this work, we give the first rigorous bounds for the efficacy of seed-chain-extend with k -mers in expectation . Assume we are given a random nucleotide sequence of length ∼ n that is indexed (or seeded) and a mutated substring of length ∼ m ≤ n with mutation rate θ < 0.206. We prove that we can find a k = Θ(log n ) for the k -mer size such that the expected runtime of seed-chain-extend under optimal linear-gap cost chaining and quadratic time gap extension is O ( mn f (θ) log n ), where f (θ) < 2.43 · θ holds as a loose bound. The alignment also turns out to be good; we prove that more than 1 − O ( 1 m ) fraction of the homologous bases is recoverable under an optimal chain. We also show that our bounds work when k -mers are sketched , that is, only a subset of all k -mers is selected, and that sketching reduces chaining time without increasing alignment time or decreasing accuracy too much, justifying the effectiveness of sketching as a practical speedup in sequence alignment. We verify our results in simulation and on real noisy long-read data and show that our theoretical runtimes can predict real runtimes accurately. We conjecture that our bounds can be improved further, and in particular, f (θ) can be further reduced.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.088 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.007 | 0.015 |
| Open science | 0.005 | 0.006 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.008 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".