Gaussian Process Modeling and Supervised Dimensionality Reduction Algorithms via Stiefel Manifold Learning
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Bibliographic record
Abstract
Much research has gone into scaling up classical machine learning algorithms such as\nGaussian Processes (GPs), but the curse of dimensionality still remains. While many\nsupervised dimensionality reduction algorithms have been proposed in the literature, few\nof them can scale up to large data-sets. Furthermore, the majority of dimensionality\nreduction techniques are tailored for classication problems, which leaves regression tasks\nunexplored. The contributions of this thesis are threefold. First, we extend classical active\nsubspace (AS) theory to a non-linear counterpart. Secondly, we introduce a scalable non\nlinear supervised principal component analysis (SPCA) algorithm. Thirdly, we propose a\nnovel class of supervised dimensionality reduction algorithms called smoothening analysis\n(SA). The SA algorithms consist of scalable linear and non-linear frequentist and Bayesian\nalgorithms tailored (but not limited) for regression tasks that learn low dimensional Stiefel\nmanifolds.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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