Gaussian processes and other kernel methods
Why this work is in the frame
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Bibliographic record
Abstract
The theory of kernels offers a rich mathematical framework for the archetypical tasks of classification and regression. Its core insight consists of the representer theorem that asserts that an unknown target function underlying a dataset can be represented by a finite sum of evaluations of a singular function, the so-called kernel function. Together with the infamous kernel trick that provides a practical way of incorporating such a kernel function into a machine learning method, a plethora of algorithms can be made more versatile. This chapter first introduces the mathematical foundations required for understanding the distinguished role of the kernel function and its consequence in terms of the representer theorem. Afterwards, we show how selected popular algorithms, including Gaussian processes, can be promoted to their kernel variant. In addition, several ideas on how to construct suitable kernel functions are provided, before demonstrating the power of kernel methods in the context of quantum (chemistry) problems.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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