Parallel computation of high dimensional robust correlation and covariance matrices
Bibliographic record
Abstract
The computation of covariance and correlation matrices are critical to many data mining applications and processes. Unfortunately the classical covariance and correlation matrices are very sensitive to outliers. Robust methods, such as QC and the Maronna method, have been proposed. However, existing algorithms for QC only give acceptable performance when the dimensionality of the matrix is in the hundreds; and the Maronna method is rarely used in practice because of its high computational cost.In this paper, we develop parallel algorithms for both QC and the Maronna method. We evaluate these parallel algorithms using a real data set of the gene expression of over 6,000 genes, giving rise to a matrix of over 18 million entries. In our experimental evaluation, we explore scalability in dimensionality and in the number of processors. We also compare the parallel behaviours of the two methods. After thorough experimentation, we conclude that for many data mining applications, both QC and Maronna are viable options. Less robust, but faster, QC is the recommended choice for small parallel platforms. On the other hand, the Maronna method is the recommended choice when a high degree of robustness is required, or when the parallel platform features a high number of processors.
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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 | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".