Model-Based Learning Using a Mixture of Mixtures of Gaussian and Uniform Distributions
Bibliographic record
Abstract
We introduce a mixture model whereby each mixture component is itself a mixture of a multivariate Gaussian distribution and a multivariate uniform distribution. Although this model could be used for model-based clustering (model-based unsupervised learning) or model-based classification (model-based semi-supervised learning), we focus on the more general model-based classification framework. In this setting, we fit our mixture models to data where some of the observations have known group memberships and the goal is to predict the memberships of observations with unknown labels. We also present a density estimation example. A generalized expectation-maximization algorithm is used to estimate the parameters and thereby give classifications in this mixture of mixtures model. To simplify the model and the associated parameter estimation, we suggest holding some parameters fixed-this leads to the introduction of more parsimonious models. A simulation study is performed to illustrate how the model allows for bursts of probability and locally higher tails. Two further simulation studies illustrate how the model performs on data simulated from multivariate Gaussian distributions and on data from multivariate t-distributions. This novel approach is also applied to real data and the performance of our approach under the various restrictions is discussed.
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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 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".