Solving a large-scale least squares problem with a simplex constraint by a two-stage algorithm
Bibliographic record
Abstract
In this paper, we introduce a two-stage algorithm for a large-scale least squares problem with a simplex constraint.The basic idea is to use the accelerated proximal gradient (APG) method to generate a relatively good precision solution for the primal problem, and take this point as the initial point of the second stage.In the second stage, we use the semismooth Newton (SsN) based on the augmented Lagrangian method (ALM) to solve the dual problem, that is, the ALM is used to solve the dual problem, and the SsN method is used to solve the subproblem.It is worth mentioning that, due to the piecewise linearity of the subproblem, the accuracy of the SsN method decreases relatively slowly in the early stage, and the APG method can effectively reduce the time required in this stage.In addition, we also prove the convergence and convergence rate of the proposed algorithm under certain conditions.Numerical experiments demonstrate that our algorithm outperforms the current state-of-the-art algorithms for the least squares problem with a simplex constraint.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 0.003 |
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".