Order Selection in Finite Mixture Models With a Nonsmooth Penalty
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Bibliographic record
Abstract
AbstractOrder selection is a fundamental and challenging problem in the application of finite mixture models. In this article, we develop a new penalized likelihood approach. The new method, modified smoothly clipped absolute deviation (MSCAD), deviates from information-based methods such as Akaike information criterion (AIC) and Bayesian information criterion (BIC) by introducing two penalty functions that depend on the mixing proportions and the component parameters. It is consistent at estimating both the order of the mixture model and the mixing distribution. Simulations show that MSCAD has much better performance than a number of existing methods. Two real-data examples are examined to illustrate the performance of MSCAD.KEY WORDS: Expectation-maximization (EM) algorithmFinite mixture modelPenalty methodSmoothly clipped absolute deviation (SCAD)
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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