A cyclic algorithm for maximum likelihood estimation using Schur complement
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Bibliographic record
Abstract
Summary Using the Schur complement of a matrix, we propose a computational framework for performing constrained maximum likelihood estimation in which the unknown parameters can be partitioned into two sets. Under appropriate regularity conditions, the corresponding estimating equations form a non‐linear system of equations with constraints. Solving this system is typically accomplished via methods which require computing or estimating a Hessian matrix. We present an alternative algorithm that solves the constrained non‐linear system in block coordinate descent fashion. An explicit form for the solution is given. The overall algorithm is shown in numerical studies to be faster than standard methods that either compute or approximate the Hessian as well as the classical Nelder–Mead algorithm. We apply our approach to a motivating problem of evaluating the effectiveness of Road Safety Policies. This includes several numerical studies on simulated data. Copyright © 2015 John Wiley & Sons, Ltd.
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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 | 0.000 | 0.000 |
| 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) | 0.000 | 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