Robust Multi-Model Subset Selection
Bibliographic record
Abstract
Outlying observations can be challenging to handle and adversely affect subsequent analyses, especially in data with increasing dimensional complexity. Although outliers are not always undesired anomalies in the data and may possess valuable insights, only methods that are robust to outliers are able to accurately identify them and resist their influence. In this paper, we propose Robust Multi-Model Subset Selection (RMSS), a method that generates an ensemble of sparse and diverse predictive models that are resistant to outliers. We show that the ensembles generally outperform single-model sparse and robust methods. Cross-validation is used to tune parameters to control levels of sparsity, diversity, and robustness. We establish the finite-sample breakdown point of the models generated by RMSS, including that of the Robust Best Subset Selection (RBSS) estimator as a special case. In addition, we develop a tailored computing algorithm to learn the ensemble by leveraging recent developments in ℓ0 optimization. Our extensive numerical experiments on synthetic and artificially contaminated real datasets from bioinformatics and cheminformatics demonstrate the competitive advantage of our method over state-of-the-art single-model methods. The Supplementary Material contains all theoretical proofs, additional algorithmic and computational details, and the code and data to reproduce our numerical results.
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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 | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| 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 | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".