Logistic Regression Confined by Cardinality-Constrained Sample and Feature Selection
Bibliographic record
Abstract
Many vision-based applications rely on logistic regression for embedding classification within a probabilistic context, such as recognition in images and videos or identifying disease-specific image phenotypes from neuroimages. Logistic regression, however, often performs poorly when trained on data that is noisy, has irrelevant features, or when the samples are distributed across the classes in an imbalanced setting; a common occurrence in visual recognition tasks. To deal with those issues, researchers generally rely on adhoc regularization techniques or model a subset of these issues. We instead propose a mathematically sound logistic regression model that selects a subset of (relevant) features and (informative and balanced) set of samples during the training process. The model does so by applying cardinality constraints (via ℓ0-`norm' sparsity) on the features and samples. ℓ0defines sparsity in mathematical settings but in practice has mostly been approximated (e.g., via ℓ1or its variations) for computational simplicity. We prove that a local minimum to the non-convex optimization problems induced by cardinality constraints can be computed by combining block coordinate descent with penalty decomposition. On synthetic, image recognition, and neuroimaging datasets, we show that the accuracy of the method is higher than alternative methods and classifiers commonly used in the literature.
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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 | 0.008 | 0.030 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".