Fast Robust Model Selection in Large Datasets
Bibliographic record
Abstract
Large datasets are increasingly common in many research fields. In particular, in the linear regression context, it is often the case that a huge number of potential covariates are available to explain a response variable, and the first step of a reasonable statistical analysis is to reduce the number of covariates. This can be done in a forward selection procedure that includes selecting the variable to enter, deciding to retain it or stop the selection, and estimating the augmented model. Least squares plus t tests can be fast, but the outcome of a forward selection might be suboptimal when there are outliers. In this article we propose a complete algorithm for fast robust model selection, including considerations for huge sample sizes. Because simply replacing the classical statistical criteria with robust ones is not computationally possible, we develop simplified robust estimators, selection criteria, and testing procedures for linear regression. The robust estimator is a one-step weighted M-estimator that can be biased if the covariates are not orthogonal. We show that the bias can be made smaller by iterating the M-estimator one or more steps further. In the variable selection process, we propose a simplified robust criterion based on a robust t statistic that we compare with a false discovery rate-adjusted level. We carry out a simulation study to show the good performance of our approach. We also analyze two datasets and show that the results obtained by our method outperform those from robust least angle regression and random forests. Supplemental materials are available online.
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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 | 0.037 | 0.100 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".