Approximation algorithms for speeding up dynamic programming and denoising aCGH data
Why this work is in the frame
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Bibliographic record
Abstract
The development of cancer is largely driven by the gain or loss of subsets of the genome, promoting uncontrolled growth or disabling defenses against it. Denoising array-based Comparative Genome Hybridization (aCGH) data is an important computational problem central to understanding cancer evolution. In this article, we propose a new formulation of the denoising problem that we solve with a “vanilla” dynamic programming algorithm, which runs in O ( n 2 ) units of time. Then, we propose two approximation techniques. Our first algorithm reduces the problem into a well-studied geometric problem, namely halfspace emptiness queries, and provides an ϵ additive approximation to the optimal objective value in Õ( n 4/3;+Δ log (U/ϵ)) time, where Δ is an arbitrarily small positive constant and U = max{#8730;C,(| P i |) i =1,…, n } ( P =( P 1 , P 2 , …, P n ), P i ∈ ℝ, is the vector of the noisy aCGH measurements, C a normalization constant). The second algorithm provides a (1 ± ϵ) approximation (multiplicative error) and runs in O ( n log n /ϵ) time. The algorithm decomposes the initial problem into a small (logarithmic) number of Monge optimization subproblems that we can solve in linear time using existing techniques. Finally, we validate our model on synthetic and real cancer datasets. Our method consistently achieves superior precision and recall to leading competitors on the data with ground truth. In addition, it finds several novel markers not recorded in the benchmarks but supported in the oncology literature.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it