Dominating Hyperplane Regularization for Variable Selection in Multivariate Count Regression
Bibliographic record
Abstract
Identifying relevant factors that influence the multinomial counts in compositional data is difficult in high dimensional settings due to the complex associations and overdispersion. Multivariate count models such as the Dirichlet-multinomial (DM), negative multinomial, and generalized DM accommodate overdispersion but are difficult to optimize due to their non-concave likelihood functions. Further, for the class of regression models that associate covariates to the multivariate count outcomes, variable selection becomes necessary as the number of potentially relevant factors becomes large. The sparse group lasso (SGL) is a natural choice for regularizing these models. Motivated by understanding the associations between water quality and benthic macroinvertebrate compositions in Canada's Athabasca oil sands region, we develop dominating hyperplane regularization (DHR), a novel method for optimizing regularized regression models with the SGL penalty. Under the majorization-minimization framework, we show that applying DHR to a SGL penalty gives rise to a surrogate function that can be expressed as a weighted ridge penalty. Consequently, we prove that for multivariate count regression models with the SGL penalty, the optimization leads to an iteratively reweighted Poisson ridge regression. We demonstrate stable optimization and high performance of our algorithm through simulation and real world application to benthic macroinvertebrate compositions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".