Minimax robust active learning for approximately specified regression models
Bibliographic record
Abstract
Abstract We address problems of model misspecification in active learning. We suppose that an investigator will sample training input points (predictors) from a subpopulation with a chosen distribution, possibly different from that generating the underlying whole population. This is in particular justified when full knowledge of the predictors is easily acquired, but determining the responses is expensive. Having sampled the responses the investigator will estimate a, possibly incorrectly specified, regression function and then predict the responses at all remaining values of the predictors. We derive functions of the predictors , and carry out probability weighted sampling with weights proportional to . The functions are asymptotically minimax robust against the losses incurred by random measurement error in the responses, sampling variation in the inputs, and biases resulting from the model misspecification. In our applications the values of are functions of the diagonal elements of the “hat” matrix which features in a regression on the entire population; this yields an interpretation of sampling the “most influential” part of the population. Applications on simulated and benchmark data sets demonstrate the strong gains to be achieved in this manner, relative to passive learning and to previously proposed methods of active learning. We go on to illustrate the methods in the context of a case study relating ice thickness and snow depth at various locations in Canada, using a “population” of about 50,000 observations made available by Statistics Canada. The Canadian Journal of Statistics 46: 104–122; 2018 © 2017 Statistical Society of Canada
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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 | 0.016 | 0.043 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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".