Construction of A-optimal Designs for Linear Models
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Bibliographic record
Abstract
For estimating parameters of a statistical model, it is important to minimize the variances of the estimators. Efficiency of an estimator increases as its variance becomes smaller. Sometimes instead of minimizing the variances of the individual parameters, it is important to minimize the total or average variance of all the parameter estimators. This refers to A-optimality in the context of optimal experimental design. Motivated by this fact, we construct A-optimal designs for some regression models using a class of algorithms, indexed by a function which depends on the derivatives of the criterion function. We also develop strategies for constructing A-optimal designs and investigate techniques for improving convergence rates by using the properties of the directional derivatives of the criterion function. We explored the design construction through some examples including one practical problem arising in chemistry.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 it