Low-rank matrix recovery under heavy-tailed errors
Why this work is in the frame
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Bibliographic record
Abstract
This paper proposes convex relaxation based robust methods to recover approximately low-rank matrices in the presence of heavy-tailed and asymmetric errors, allowing for heteroscedasticity. We focus on three archetypal applications in matrix recovery: matrix compressed sensing, matrix completion and multitask regression. Statistically, we provide sub-Gaussian-type deviation bounds when the noise variables only have bounded variances in each aforementioned setting. Improving upon the earlier results in Fan, Wang and Zhu (Ann. Statist. 49 (2021) 1239–1266), the convergence rates of our estimators are proportional to the noise scale under matrix sensing and multitask regression settings, and thus diminish to 0 in the noiseless case. Computationally, we propose a matrix version of the local adaptive majorize-minimization algorithm, which is much faster than the alternating direction method of multiplier used in previous work and is scalable to large datasets. Numerical experiments demonstrate the advantage of our methods over their non-robust counterparts and corroborate the theoretical findings that the convergence rates are proportional to the noise scale.
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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 | 0.001 |
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 it