Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials
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Bibliographic record
Abstract
Previous work has examined structure learning in log-linear models with `1-regularization, largely focusing on the case of pairwise potentials. In this work we con-sider the case of models with potentials of arbitrary order, but that satisfy a hierarchi-cal constraint. We enforce the hierarchical constraint using group `1-regularization with overlapping groups. An active set method that enforces hierarchical inclusion allows us to tractably consider the exponential num-ber of higher-order potentials. We use a spectral projected gradient method as a sub-routine for solving the overlapping group `1-regularization problem, and make use of a sparse version of Dykstra’s algorithm to com-pute the projection. Our experiments indi-cate that this model gives equal or better test set likelihood compared to previous models. 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 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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