A fast and effective algorithm for sparse linear regression with $\ell_p$-norm data fidelity and elastic net regularization
Bibliographic record
Abstract
Elastic net model is widely used in high-dimensional statistics for parameter regression and variable selection, which has been proved that the performance is often better than the lasso.However, it can only deals with data containing Gaussian noise, so it is not suitable for modern complex highdimensional data.Fortunately, an adaptive and robust minimization model, which combines the ℓ p -norm data fidelity and elastic net regularization, has been proposed to deal with different types of noises and inherit the advantages of the elastic net in prediction accuracy.The double non-smoothness in objective function makes it challenging to minimize the model.After investigation, we find that the optimization algorithm is currently limited to the first-order alternating direction method of multipliers (ADMM), which is relatively lower in the recovered solutions' accuracy and relatively slower in the calculation speed.Therefore, we are committed to developing a fast and effective algorithm based on second-order information.Specifically, we propose a preconditioned proximal point algorithm (abbreviated as P-PPA) to solve the considered model by adding a proximal term.In theory, we analyze the consistency between the solution of the surrogate model and the original model.In addition, a key subproblem in P-PPA is solved by superlinear or even quadratically convergent semismooth Newton methods from the dual perspective.Finally, a large number of numerical experiments on high-dimensional simulated and real examples fully verify that our proposed algorithm is superior to ADMM in terms of calculation accuracy and speed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".