A constrained LiGME model and its proximal splitting algorithm under overall convexity condition
Bibliographic record
Abstract
The convex optimization has been used for modeling of many estimation problems in data science and engineering, where convex constraint sets in such a model express respectively a priori knowledge regarding a certain unknown vector to be estimated.The LiGME model was established recently in [J.Abe, M. Yamagishi, I. Yamada, Linearly involved generalized Moreau enhanced models and their proximal splitting algorithm under overall convexity condition, Inverse Probl.36 (2020), 035012] for a sound utilization of linearly involved regularizers closer to certain ideal discrete measures, for sparsity as well as for low-rankness, than their convex envelopes.Despite of the nonconvexity of linearly involved regularizers, the LiGME model can keep the overall convexity of its optimization model with a strategic parameter tuning.In this paper, for flexible exploitation of multiple convex constraint sets, we propose a constrained LiGME (cLiGME) model as an enhancement of the original LiGME model.Within the frame of convex optimization, the proposed cLiGME model can promote such desired features more strategically than standard models using convex regularizers, as well as can admit multiple linearly involved convex indicator functions for hard constraints.We also propose a proximal splitting type algorithm for the cLiGME model and demonstrate its effectiveness with a simple numerical experiment.The cLiGME model can be seen as an integration of central ideas in the LiGME model and the set theoretic estimation.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".