LD Matrix Approximations for Scalable Analysis of High-dimensional Genetic Data
Bibliographic record
Abstract
Abstract Linkage disequilibrium (LD) matrices are an essential part of many statistical genetics methods. However, their high dimensionality makes their computation and storage impractical for large genomic data. Common sparse approximations, such as banded matrices, come at the expense of losing the positive semi-definite (PSD) property, a critical quality that ensures numerical stability of many downstream analyses. Conversely, methods that guarantee a PSD approximation, like block-diagonal approaches, require coarse approximations of the LD structure. In this work, we present a novel method to approximate an LD matrix with a sparse, banded matrix that is guaranteed to be PSD while preserving the correlation structure within the band. This is done via a reformulation of the nearest correlation matrix problem using the Cholesky decomposition, which implicitly imposes the PSD property in a highly scalable parallel approach. On whole-chromosome data from the 1000 Genomes Project and the UK Biobank, our method builds sparse positive semi-definiteness that are more more accurate than either block-diagonal or shrinkage estimators.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".