OCMA: Fast, Memory-Efficient Factorization of Prohibitively Large Relationship Matrices
Bibliographic record
Abstract
Abstract Matrices representing genetic relatedness among individuals (i.e., Genomic Relationship Matrices, GRMs) play a central role in genetic analysis. The eigen-decomposition of GRMs (or its alternative that generates fewer top singular values using genotype matrices) is a necessary step for many analyses including estimation of SNP-heritability, Principal Component Analysis (PCA), and genomic prediction. However, the GRMs and genotype matrices provided by modern biobanks are too large to be stored in active memory. To accommodate the current and future “bigger-data”, we develop a disk-based tool, Out-of-Core Matrices Analyzer (OCMA), using state-of-the-art computational techniques that can nimbly perform eigen and Singular Value Decomposition (SVD) analyses. By integrating memory mapping (mmap) and the latest matrix factorization libraries, our tool is fast and memory-efficient. To demonstrate the impressive performance of OCMA, we test it on a personal computer. For full eigen-decomposition, it solves an ordinary GRM (N = 10,000) in 55 sec. For SVD, a commonly used faster alternative of full eigen-decomposition in genomic analyses, OCMA solves the top 200 singular values (SVs) in half an hour, top 2,000 SVs in 0.95 hr, and all 5,000 SVs in 1.77 hr based on a very large genotype matrix (N = 1,000,000, M = 5,000) on the same personal computer. OCMA also supports multi-threading when running in a desktop or HPC cluster. Our OCMA tool can thus alleviate the computing bottleneck of classical analyses on large genomic matrices, and make it possible to scale up current and emerging analytical methods to big genomics data using lightweight computing resources.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.021 | 0.008 |
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".