Grouped Spherical Data Modeling Through Hierarchical Nonparametric Bayesian Models and Its Application to fMRI Data Analysis
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Bibliographic record
Abstract
normalized vectors) modeling has become a promising research topic in various real-world applications (such as gene expression data analysis, document categorization, and gesture recognition). In this work, we propose a hierarchical nonparametric Bayesian model based on von Mises-Fisher (VMF) distributions for modeling spherical data that involve multiple groups, where each observation within a group is sampled from a VMF mixture model with an infinite number of components allowing them to be shared across groups. Our model is formulated by employing a hierarchical nonparametric Bayesian framework known as the hierarchical Pitman-Yor (HPY) process mixture model, which possesses a power-law nature over the distribution of the components and is particularly useful for data distributions with heavy tails and skewness. To learn the proposed HPY process mixture model with VMF distributions, we systematically develop a closed-form optimization algorithm based on variational Bayes (VB). The merits of the proposed hierarchical Bayesian nonparametric model for modeling grouped spherical data are demonstrated through experiments on both synthetic data and a real-world application about resting-state functional magnetic resonance imaging (fMRI) data analysis.
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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 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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