A New Smooth Approximation to the Zero One Loss with a Probabilistic\n Interpretation
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Bibliographic record
Abstract
We examine a new form of smooth approximation to the zero one loss in which\nlearning is performed using a reformulation of the widely used logistic\nfunction. Our approach is based on using the posterior mean of a novel\ngeneralized Beta-Bernoulli formulation. This leads to a generalized logistic\nfunction that approximates the zero one loss, but retains a probabilistic\nformulation conferring a number of useful properties. The approach is easily\ngeneralized to kernel logistic regression and easily integrated into methods\nfor structured prediction. We present experiments in which we learn such models\nusing an optimization method consisting of a combination of gradient descent\nand coordinate descent using localized grid search so as to escape from local\nminima. Our experiments indicate that optimization quality is improved when\nlearning meta-parameters are themselves optimized using a validation set. Our\nexperiments show improved performance relative to widely used logistic and\nhinge loss methods on a wide variety of problems ranging from standard UC\nIrvine and libSVM evaluation datasets to product review predictions and a\nvisual information extraction task. We observe that the approach: 1) is more\nrobust to outliers compared to the logistic and hinge losses; 2) outperforms\ncomparable logistic and max margin models on larger scale benchmark problems;\n3) when combined with Gaussian- Laplacian mixture prior on parameters the\nkernelized version of our formulation yields sparser solutions than Support\nVector Machine classifiers; and 4) when integrated into a probabilistic\nstructured prediction technique our approach provides more accurate\nprobabilities yielding improved inference and increasing information extraction\nperformance.\n
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it