Clustering Gaussian Processes: A Modified EM Algorithm for Functional Data Analysis with Application to British Columbia Coastal Rainfall Patterns
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Bibliographic record
Abstract
Functional data analysis is a statistical framework where data are assumed to follow some functional form. This method of analysis is commonly applied to time series data, where time, measured continuously or in discrete intervals, serves as the lo- cation for a function’s value. In this thesis Gaussian processes, a generalization of the multivariate normal distribution to function space, are used. When multiple processes are observed on a comparable interval, clustering them into sub-populations can provide significant insights. A modified EM algorithm is developed for cluster- ing processes. The model presented clusters processes based on how similar their underlying covariance kernel is. In other words, cluster formation arises from modelling correlation between inputs (as opposed to magnitude between process values). The method is applied to both simulated data and British Columbia coastal rainfall patterns. Results show clustering yearly processes can accurately classify extreme weather patterns.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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