Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions
Bibliographic record
Abstract
The mixture‐of‐experts (MoE) paradigm attempts to learn complex models by combining several “experts” via probabilistic mixture models. Each expert in the MoE model handles a small area of the data space in which a gating function controls the data‐to‐expert assignment. The MoE framework has been used extensively in designing non‐linear models in machine learning and statistics to model the heterogeneity in data for the purpose of regression, classification and clustering. The existing MoE of multi‐target regression (MoE‐MTR) models for continuous data is based on multivariate normal distributions. However, in many practical situations, for a set of data, a group or groups of observations may exhibit asymmetric and heavy‐tailed behaviour, and inference based on symmetric distributions in such situations can unduly affect the fit of the regression model. We introduce here a novel robust multivariate non‐normal MoE model by the use of mean mixture of normal distributions. The proposed model can handle the issues of MoE‐MTR models regarding possibly skewed, heavy‐tailed and noisy data. Maximum likelihood estimates of model parameters are developed based on an expectation‐maximization (EM)‐type algorithm. Parsimony is also obtained by imposing suitable constraints on the expert dispersion matrices. The usefulness of the proposed methodology is illustrated using simulated and real data sets.
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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 | 0.009 | 0.025 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.003 |
| 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".