Fully polynomial-time randomized approximation schemes for global optimization of high-dimensional minimax concave penalized generalized linear models
Bibliographic record
Abstract
Global solutions to high-dimensional sparse estimation problems with a folded concave penalty (FCP) have been shown to be statistically desirable but are strongly NP-hard to compute which implies the non-existence of pseudo-polynomial time global optimization schemes in the worst case.This paper shows that, with high probability, a global solution to generalized linear models with minimax concave penalty (MCP), a specific type of FCP, coincides with a stationary point characterized by the significant subspace second order necessary conditions (S 3 ONC).Given that the desired S 3 ONC solution admits a fully polynomial-time randomized approximation scheme (FPRAS), we are able to demonstrate the existence of an FPRAS for this strongly NP-hard problem.We further demonstrate two versions of the FPRAS for generating the desired S 3 ONC solutions.One follows the paradigm of an interior point trust region algorithm and the other is the well-studied local linear approximation (LLA).Our analysis thus provides new techniques for global optimization of certain NP-Hard problems and new insights on the effectiveness of LLA.
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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 | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 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".