Piecewise bounds for estimating bernoulli-logistic latent Gaussian models
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Bibliographic record
Abstract
Bernoulli-logistic latent Gaussian models (bLGMs) are a useful model class, but accurate parameter estimation is complicated by the fact that the marginal likelihood contains an intractable logistic-Gaussian integral. In this work, we propose the use of fixed piecewise linear and quadratic upper bounds to the logistic-log-partition (LLP) function as a way of circumventing this intractable integral. We describe a framework for approximately computing minimax optimal piecewise quadratic bounds, as well a generalized expectation maximization algorithm based on using piecewise bounds to estimate bLGMs. We prove a theoretical result relating the maximum error in the LLP bound to the maximum error in the marginal likelihood estimate. Finally, we present empirical results showing that piecewise bounds can be significantly more accurate than previously proposed variational bounds. 1.
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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 | 0.001 |
| Open science | 0.001 | 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