Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables
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Bibliographic record
Abstract
We address component-based regularization of a multivariate generalized linear model (GLM). A vector of random responses [Formula: see text] is assumed to depend, through a GLM, on a set [Formula: see text] of explanatory variables, as well as on a set [Formula: see text] of additional covariates. [Formula: see text] is partitioned into [Formula: see text] conceptually homogenous variable groups [Formula: see text], viewed as explanatory themes. Variables in each [Formula: see text] are assumed many and redundant. Thus, generalized linear regression demands dimension reduction and regularization with respect to each [Formula: see text]. By contrast, variables in [Formula: see text] are assumed few and selected so as to demand no regularization. Regularization is performed searching each [Formula: see text] for an appropriate number of orthogonal components that both contribute to model [Formula: see text] and capture relevant structural information in [Formula: see text]. To estimate a single-theme model, we first propose an enhanced version of Supervised Component Generalized Linear Regression (SCGLR), based on a flexible measure of structural relevance of components, and able to deal with mixed-type explanatory variables. Then, to estimate the multiple-theme model, we develop an algorithm encapsulating this enhanced SCGLR: THEME-SCGLR. The method is tested on simulated data and then applied to rainforest data in order to model the abundance of tree species.
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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