Gaussian Variational Approximation with Composite Likelihood for Crossed Random Effect Models
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Bibliographic record
Abstract
Composite likelihood usually ignores dependencies among response components, while variational approximation to likelihood ignores dependencies among parameter components.What both methods have in common is that they essentially break the dependence of random effects.In this paper, we derive a Gaussian variational approximation to the composite log-likelihood function for Poisson and Gamma models with crossed random effects.We present theoretical aspects of the estimates derived from this approximation and support these theories with simulation studies.Specifically, we show the estimates are consistent with a convergence rate m -1/2 +n -1/2 , where m and n denote the number of rows and columns, respectively.We further provide detailed asymptotic normality results under a new regime where log m/ log n for (1/2, 2).Additional simulation studies show that our method yields comparable estimation performance and is slightly faster than the Laplace approximation in the package glmmTMB and a Gaussian variational approximation to the full log-likelihood function.
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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