A Dimension-Independent Generalization Bound for Kernel Supervised Principal Component Analysis
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Bibliographic record
Abstract
Kernel supervised principal component analysis (KSPCA) is a computationally ecient supervised feature extraction method that can learn non-linear transformations. We start the study of the statistical properties of KSPCA, providing the rst bound on its sample complexity. This bound is dimension-independent, which justies the good performance of KSPCA on high-dimensional data. Another observation is that in the kernelized version, the number of parameters of KSPCA grows linearly with the sample size. While this potentially increases the risk of over-tting, KSPCA works well in practice. In this work, we justify this compelling characteristic of KSPCA by providing a guarantee indicating that KSPCA generalizes well even when the number of parameters is large, as long as they have small norms.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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